User:Moudster/sandbox

Stephen T. Hedetniemi
Stephen Hedetniemi is an American Mathematician. His interests includeGraph theory, Design and Analysis of algorithms, and Computation Theory. He developed Hedetniemi's conjecture.

Education and Career
Hedetniemi graduated from University of Michigan with a Bachelor's of Science in Mathematics in 1960, a Master's of Science in Communications Sciences in 1962 and a Ph. D. in Communication Sciences in 1966. His dissertation, Homomorphisms of Graphs and Automata, was supervised by Frank Harary.

After earning his Ph. D., Hedetniemi had a short stint working for the Naval Surface Warfare Center before going on to teach at several universities including the University of Michigan, University of Iowa, University of Victoria, University of Virginia, University of Oregon, and Clemson University where he is currently a Professor in the Department of Computer Science.

Publications
1963

[1]        B. Levin and S. Hedetniemi. Determining fastest routes using fixed schedules. ''AFIPS Conf. Proc.'' 23:1-8, 1963.

1967

[2]        F. Harary, S. Hedetniemi and G. Prins. An interpolation theorem for graphical  homomorphisms. ''Portugal. Math.'' 26:453-462,1967.

1968

[3]        G. Chartrand, D. Geller and S. Hedetniemi. A generalization of the chromatic number. ''Proc. Camb. Philos. Soc.'' 64:265-271, 1968.

[4]        S. Hedetniemi. On partitioning planar graphs. ''Canad. Math. Bull.'' 11:203-211, 1968.

[5]        S. Hedetniemi. On minimum walks in graphs. Naval Res. Logistics Quarterly 15:453- 458, 1968.

1969

[6]        F. Harary, S. Hedetniemi, and R. Robinson. Uniquely colorable graphs. ''J. Combin. Theory'' 6:264-270, 1969.

[7]        D. Geller and S. Hedetniemi, A proof technique in graph theory, in Proof Techniques in Graph Theory, F. Harary, Ed., Academic Press, New York, 49-59, 1969.

[8]        S. Hedetniemi. On classes of graphs defined by special cutsets of lines. In The Many Facets of Graph Theory, G. Chartrand and S.F. Kapoor, Eds., Springer-Verlag, Berlin, 171-189, 1969.

[9]        S. Hedetniemi. A note on a category of graphs. In The Many Facets of Graph Theory, G. Chartrand and S.F. Kapoor, Eds., Springer-Verlag, Berlin, 89-90, 1969.

1970

[10]      F. Harary and S. Hedetniemi. The achromatic number of a graph. ''J. Combin. Theory'' 8:154-161, 1970.

[11]      S. Hedetniemi. Disconnected colorings of graphs. In Combinatorial Structures and Their Applications, R. Guy, H. Hanani, N. Sauer, and J. Schonheim, Eds., Gordon and       Breach, New York, 163-167, 1970.

1971

[12]      G. Chartrand, D. Geller, and S. Hedetniemi. Graphs with forbidden subgraphs. ''J. Combin. Theory'' 10:12-41, 1971.

[13]      S. Hedetniemi. Graphs of (0,1)-matrices. In Recent Trends in Graph Theory, M. Capobianco, J.B. Frechen and M. Krolik, Eds., Springer-Verlag, Berlin, 157-172, 1971.

[14]      S. Hedetniemi. Characterizations and constructions of minimally 2- connected graphs and minimally strong digraphs. ''Proc. Second Louisiana Conf. on Combinatorics, Graph Theory and Computing, Util. Math''., Winnipeg, 257-282, 1971.

1972

[15]      A.C. Fleck, S.T. Hedetniemi, and R.H. Oehmke. S-semigroups of automata. ''J. Assoc. Comput. Mach.'' 19:3-10, 1972.

[16]      S.T. Hedetniemi and P.J. Slater. Line graphs of triangleless graphs and iterated clique graphs. In Graph Theory and Applications, Y. Alavi, D.R. Lick, and A.T. White, Eds.,     Springer-Verlag, Berlin, 139-149, 1972.

[17]      E.J. Cockayne and S.T. Hedetniemi. Interpolation systems. ''Proc. Third Southeastern Conf. on Combinatorics, Graph Theory and Computing'', Util. Math, Winnipeg, 117-129,      1972.

1973

[18]      S. Hedetniemi. Hereditary properties of graphs. ''J. Combin. Theory,'' 14:94-99, 1973.

[19]      S.E. Goodman and S.T. Hedetniemi. Eulerian walks in graphs. SIAM J. Comput. 2:16-    27, 1973.

1974

[20]      S.E. Goodman and S.T. Hedetniemi. Sufficient conditions for a graph to be Hamiltonian. ''J. Combin. Theory'' 16:175-180, 1974.

[21]      S.E. Goodman and S.T. Hedetniemi. On Hamiltonian walks in graphs. SIAM J. Comput. 3:214-221, 1974.

[22]      S.E. Goodman, S.T. Hedetniemi, and P.J. Slater. Some results on the optional and non- optional Hamiltonian completion problem. ''Proc. Fifth Southeastern Conf. on             Combinatorics, Graph Theory and Computing, Util. Math''., Winnipeg, 423-448, 1974.

[23]      E.J. Cockayne and S.T. Hedetniemi. Independence graphs. ''Proc. Fifth Southeastern Conf. on Combinatorics, Graph Theory and Computing, Util. Math''., Winnipeg, 471-491,      1974.

[24]      S.E. Goodman and S.T. Hedetniemi. On the Hamiltonian completion problem. In Graphs and Combinatorics, 1973, R.A. Bari and F. Harary, Eds., Springer-Verlag, Berlin, 262-     272, 1974.

1975

[25]      S.E. Goodman, S.T. Hedetniemi, and P.J. Slater. Advances on the Hamiltonian completion problem. ''J. Assoc. Comput. Mach.'' 22:352-360, 1975.

[26]      E.J. Cockayne, S.E. Goodman, and S.T. Hedetniemi, A linear algorithm for the domination number of a tree. ''Inform. Process. Lett.'' 4:41-44, 1975.

[27]      E.J. Cockayne and S.T. Hedetniemi. Optimal domination in graphs. ''IEEE Trans. Circuits Systems CAS'' 22:855-857, 1975.

[28]      S. Mitchell, S. Hedetniemi, and S. Goodman. Some linear algorithms on trees. ''Proc. Sixth Southeastern Conf. on Combinatorics, Graph Theory and Computing, Util. Math''.,   Winnipeg, 467-483, 1975.

1976

[29]      E.J. Cockayne and S.T. Hedetniemi. Disjoint independent dominating sets in graphs. Discrete Math. 15:213-222, 1976.

[30]      E.J. Cockayne and S.T. Hedetniemi. Which trees do not have disjoint maximal matchings? ''Util. Math.'' 9:329-337, 1976.

[31]      P.J. Slater, S.E. Goodman and S.T. Hedetniemi. On the optional Hamiltonian completion problem. Networks 6:35-51, 1976.

[32]      S. Goodman, S. Hedetniemi and R.E. Tarjan. B-matchings in trees. SIAM J. Comput. 5:104-107, 1976.

[33]      E.J. Cockayne and S.T. Hedetniemi. Graphes de groupes avec cliques maximales disjointes. Colloques Internationaux C.N.R.S. No. 260, Problems Combinatoires et                         des Graphes, Orsay, 81-82, 1976.

[34]      E.J. Cockayne and S.T. Hedetniemi. A linear algorithm for the maximum weight of an independent set in a tree. ''Proc. Seventh Southeastern Conf. on Combinatorics, Graph             Theory and Computing,'' Util. Math., Winnipeg, 217-228, 1976.

1977

[35]      S.E. Goodman and S.T. Hedetniemi. Introduction to the Design and Analysis of Algorithms. McGraw-Hill, New York, 371 pp., 1977.

[36]      E.J. Cockayne and S.T. Hedetniemi. Towards a theory of domination in graphs. Networks 7:247-261, 1977.

[37]      S.T. Hedetniemi and D.M. Spresser. A property of trees in terms of unique connected subgraphs. J. Graph Theory 1:335-338, 1977.

[38]      T. Beyer, A. Proskurowski, S. Hedetniemi, and S. Mitchell. Independent domination in trees, ''Proc. Eighth Southeastern Conf. on Combinatorics, Graph Theory and Computing,       Util. Math''., Winnipeg, 321-328, 1977.

[39]      S. Mitchell and S. Hedetniemi. Edge domination in trees. ''Proc. Eighth Southeastern Conf. on Combinatorics, Graph Theory and Computing, Util. Math''., Winnipeg, 489-511,      1977.

1978

[40]      E.J. Cockayne and S.T. Hedetniemi. Disjoint cliques in regular graphs of degree seven and eight. ''J. Combin. Theory'' 34:233-237, 1978.

[41]      E.J. Cockayne, B.L. Hartnell,  and S.T. Hedetniemi. A linear algorithm for disjoint matchings in trees. Discrete Math. 21:129-136, 1978.

[42]      E.J. Cockayne, S.T. Hedetniemi, and D.J. Miller. Properties of hereditary hypergraphs and middle graphs, ''Canad. Math. Bull.'' 21:461-468, 1978.

[43]      A. Farley and S. Hedetniemi. Broadcasting in grid graphs. ''Proc. Ninth Southeastern Conf. on Combinatorics, Graph Theory and Computing, Util. Math''., Winnipeg, 275-288,      1978.

1979

[44]      S.E. Goodman and S.T. Hedetniemi. A descriptive introduction to graph theory and some of its applications. Chapter 1 in Computers in Language Research, W.A. Sedelow and             S.Y. Sedelow, Eds. Mouton, The Hague, 19-95, 1979.

[45]      E.J. Cockayne, S.T. Hedetniemi, and P.J. Slater. Matchings and transversals in  hypergraphs, domination and independence in trees. ''J. Combin. Theory'' 26:78-80, 1979.

[46]      S.L. Mitchell, E.J. Cockayne, and S.T. Hedetniemi. Linear algorithms on recursive representations of trees. ''J. Comput. System Sci.'' 18:76-85, 1979.

[47]      A. Farley, S. Hedetniemi, S. Mitchell, and A. Proskurowski. Minimum broadcast graphs. Discrete Math. 25:189-193, 1979.

[48]      S.L. Mitchell and S.T. Hedetniemi. Linear algorithms for edge colorings of trees and unicyclic graphs. ''Inform. Process. Lett.'' 9:110-112, 1979.

[49]      P. Chinn, S. Hedetniemi, and S. Mitchell. Multiple message broadcasting in complete graphs. ''Proc. Tenth Southeastern Conf. on Combinatorics, Graph Theory and             Computing, Util. Math''., Winnipeg, 251-260, 1979.

1980

[50]      S.L. Mitchell and S.T. Hedetniemi. A census of minimum broadcast graphs. ''J. Combin. Inform. System Sci.'' 5:119-129, 1980.

[51]      E.J. Cockayne, R.M. Dawes, and S.T. Hedetniemi. Total domination in graphs. Networks 10:211-219, 1980.

[52]      A. Farley, S. Hedetniemi, and S. Mitchell. Rectilinear Steiner trees in rectangle trees. SIAM J. Algebraic and Discrete Meth. 1:70-81, 1980.

[53]      S.M. Hedetniemi, S.T. Hedetniemi, and P.J. Slater. Which grids are Hamiltonian? ''Proc. Eleventh Southeastern Conf. on Combinatorics, Graph Theory and Computing, Util. Math''., Winnipeg, 511-524, 1980.

1981

[54]      P.J. Slater, E.J. Cockayne, and S.T. Hedetniemi. Information dissemination in trees. SIAM J. Comput. 10:692-701, 1981.

[55]      S.M. Hedetniemi, E.J. Cockayne, and S.T. Hedetniemi. Linear algorithms for the Jordan centre and path centre of a tree. J. Transportation Science 15:98-114, 1981.

[56]      S.M. Hedetniemi, S.T. Hedetniemi, and P.J. Slater. A note on packing trees into Kn. Ars Combin. 11:149-153, 1981.

[57]      A. Farley, S. Hedetniemi, and A. Proskurowski. Partitioning trees: matching, domination and maximum diameter. ''Internat. J. Comput. Info. Sciences'' 10:55-61, 1981.

[58]      T. Beyer, S.M. Hedetniemi, S.T. Hedetniemi, and A. Proskurowski. Graph traversal with minimum stack depth. ''Proc. Twelfth Southeastern Conf. on Combinatorics, Graph             Theory and Computing, Util. Math''., Winnipeg, 121-130, 1981.

1982

[59]      S.M. Hedetniemi, S.T. Hedetniemi, and P.J. Slater. Centers and medians of Cn-trees. ''Util. Math.'' 21:225-234, 1982.

[60]      S.M. Hedetniemi and S.T. Hedetniemi. Vertex and edge deletion algorithms for trees. ''J. Combin. Inform. System Sci.'' 7:125-133, 1982.

[61]      T. Beyer, S.M. Hedetniemi, and S.T. Hedetniemi. A linear algorithm for the Grundy number of a tree. ''Proc. Thirteenth Southeastern Conf. on Combinatorics, Graph Theory and Computing, Util. Math''., Winnipeg, 351-363, 1982.

1983

[62]      S.M. Hedetniemi and S.T. Hedetniemi. Reducing space and time requirements for processing trees. ''Congr. Numer.'' 40:3-22, 1983.

[63]      S.T. Hedetniemi. A max-min relationship between matchings and domination in graphs. ''Congr. Numer.'' 40:23-34, 1983.

1984

[64]      R. Laskar, J. Pfaff, S.M. Hedetniemi, and S.T. Hedetniemi. On the algorithmic complexity of total domination. ''SIAM J. Alg. Disc. Meth.'' 5:420-425, 1984.

[65]      R. Allan, R. Laskar, and S. Hedetniemi. A note on total domination. Discrete Math. 49:7-13, 1984.

[66]      S. Hedetniemi and R. Laskar. Connected domination in graphs. In Graph Theory and Combinatorics,, B. Bollobas, Ed., Academic Press, London, 209-218, 1984.

[67]      S.M. Hedetniemi, S.T. Hedetniemi, and R. Laskar. Domination in trees: models and algorithms. In Graph Theory with Applications to Algorithms and Computer Science, Y. Alavi, G. Chartrand, L. Lesniak, D.R. Lick and C.E. Wall, Eds., (Kalamazoo, Mich., Wiley-Intersci. Publ.), New York, 423-442, 1984.

[68]      G. Cheston and S. Hedetniemi. Polling in tree networks''. Proc. Second West Coast Conf. on Combinatorics, Graph Theory and Computing, (Eugene, OR, 1983), Congr. Numer.'' 41:7-20, 1984.

[69]      J. Pfaff, R. Laskar, and S. Hedetniemi. Linear algorithms for independent domination and total domination in series-parallel graphs. ''Congr. Numer.'' 45:71-82, 1984.

1985

[70]      E.J. Cockayne, E.O. Hare, S.T. Hedetniemi, and T.V. Wimer. Bounds for the domination number of grid graphs. ''Congr. Numer.'' 47:217-228, 1985.

[71]      E.O. Hare and S.T. Hedetniemi. The certificate: a canonical data structure for trees. ''Congr. Numer.'' 48:153-170, 1985.

[72]      W.R. Hare, S.T. Hedetniemi, R. Laskar, and J. Pfaff. Complete coloring parameters of graphs. ''Congr. Numer.'' 48:171-178, 1985.

[73]      S. Hedetniemi, R. Laskar, and J. Pfaff. Irredundance in graphs: a survey. ''Congr. Numer.'' 48:183-194, 1985.

[74]      T.V. Wimer, S.T. Hedetniemi, and R. Laskar. A methodology for constructing linear graph algorithms. ''Proc. Sundance Conf., (Sundance, UT, 1985), Congr. Numer.'' 50:43-   60, 1985.

[75]      W.R. Hare, E.O. Hare, and S.T. Hedetniemi. Bandwidth of grid graphs. ''Proc. Sundance Conf., (Sundance, UT, 1985), Congr. Numer.'' 50:67-76, 1985.

[76]      E.O. Hare, W.R. Hare, and S.T. Hedetniemi. Another upper bound for the bandwidth of  trees. ''Proc. Sundance Conf., (Sundance, UT, 1985), Congr. Numer.'' 50:77-84, 1985.

1986

[77]      S.T. Hedetniemi, R. Laskar, and J. Pfaff. A linear algorithm for finding a minimum dominating set in a cactus. ''Discrete Appl. Math.'' 13:287-292, 1986.

[78]      E.J. Cockayne and S.T. Hedetniemi. On the diagonal queens domination problem. ''J. Combin. Theory'' 42:137-139, 1986.

[79]      K. Peters, R. Laskar, and S. Hedetniemi. Maximal/minimal connectivity in graphs. Ars Combin. 21:59-70, 1986.

[80]      G.S. Domke, R. Laskar, S.T. Hedetniemi, and K. Peters. The partite-chromatic number of a graph. ''Congr. Numer.'' 53:235-246, 1986.

[81]      K. Peters, R. Laskar, and S.T. Hedetniemi. On the strength of a graph. ''Congr. Numer.'' 53:247-262, 1986.

[82]      S. Hedetniemi and R. Laskar. A bipartite theory of graphs: I. ''Congr. Numer.'' 55:5-14, 1986.

[83]      E.O. Hare, S.T. Hedetniemi, and W.R. Hare. Algorithms for computing the domination number of KxN complete grid graphs. ''Congr. Numer.'' 55:81-92, 1986.

1987

[84]      P. Erdös, W.R. Hare, S.T. Hedetniemi, and R. Laskar. On the equality of the Grundy and ochromatic numbers of a graph. J. Graph Theory 11(2):157-159, 1987.

[85]      E.O. Hare and S.T. Hedetniemi. A linear algorithm for computing the knight's  domination number of a KxN chessboard. ''Congr. Numer.'' 59:115-130, 1987.

[86]      E. Hare, S. Hedetniemi, R. Laskar, K. Peters, and T. Wimer. Linear time computability of combinatorial problems on generalized series-parallel graphs''. Proc. Japan-U.S. Joint           Seminar on Discrete Algorithms and Complexity Theory, (Kyoto, Japan, 1986),    Perspectives in Computing 15:437-457, Academic Press'', 1987.

1988

[87]      S.M. Hedetniemi, S.T. Hedetniemi, and A.L. Liestman. A survey of gossiping and broadcasting in communication networks. Networks 18(4):319-359, 1988.

[88]      E.J. Cockayne, S.T. Hedetniemi, and R. Laskar. Gallai theorems for graphs, hypergraphs and set systems. Discrete Math. 72:35-47, 1988.

[89]      G. Domke, S. Hedetniemi, R. Laskar, and R. Allan. Generalized packing and coverings of graphs. ''Congr. Numer.'' 62:259-270, 1988.

[90]      N. Chandrasekharan and S. Hedetniemi. Fast parallel algorithms for tree decomposing and parsing partial k-trees. ''Proc. Twenty-sixth Annual Allerton Conf. on Communication             Control and Computing,'' (Urbana, IL). 1988.

[91]      T.V. Wimer and S.T. Hedetniemi. K-terminal recursive families of graphs''. Proc. 250th Anniversary Conf. on Graph Theory, (Ft. Wayne, IN, 1986), Congr. Numer.'' 63:161-176,      1988.

[92]      G.S. Domke, R. Laskar, and S.T. Hedetniemi. The edge subchromatic number of a graph''. Proc. 250th Anniversary Conf. on Graph Theory, (Ft. Wayne, IN, 1986), Congr. Numer.'' 64:95-104, 1988.

[93]      S. Hedetniemi and R. Laskar. A bipartite theory of graphs: II''. Proc. 250th Anniversary Conf. on Graph Theory, (Ft. Wayne, IN, 1986), Congr. Numer.'' 64:137-146, 1988.

[94]      S. Hedetniemi and R. Laskar. Recent results and open problems in domination theory. In Applications of Discrete Mathematics, R.O. Ringeisen and F.S. Roberts, Eds., SIAM,  Philadelphia, 205-218, 1988.

[95]      G.S. Domke, S.T. Hedetniemi, and R.C. Laskar. Fractional packings, coverings and irredundance in graphs. ''Congr. Numer.'' 66:227-238, 1988.

[96]      G.A. Cheston, E.O. Hare, S.T. Hedetniemi, and R.C. Laskar. Simplicial graphs. ''Congr. Numer.'' 67:105-113, 1988.

1989

[97]      M.O. Alberston, R.E. Jamison, S.T. Hedetniemi, and S.C. Locke. The subchromatic number of a graph. Discrete Math. 74:33-49, 1989.

[98]      G.A. Cheston, A. Farley, S.T. Hedetniemi, and A. Proskurowski. Centering a spanning tree of a biconnected graph. ''Inform. Process. Lett.'' 32:247-250, 1989.

[99]      S.T. Hedetniemi, D.P. Jacobs, and R. Laskar. Inequalities involving the rank of a graph. ''J. Combin. Math. Combin. Comput.'' 6:173-176, 1989.

[100]    R. Laskar and S.T. Hedetniemi. On irredundance, dimension and rank of posets. ''Graph Theory and its Applications: East and West, Proc. First China-U.S.A. Internat. Graph             Theory Conf., Ann. New York Acad. Sci.'' 576:235-240, 1989.

1990

[101]    S.T. Hedetniemi and R.C. Laskar, Guest Eds. ''Topics in Domination, Annals of Discrete Mathematics, Vol. 48 and Discrete Math. 86,'' North Holland, Amsterdam, 280 pp., 1990.

[102]    S.T. Hedetniemi and R.C. Laskar. Introduction. Ibid, 3-9, 1990.

[103]    S.T. Hedetniemi and R.C. Laskar. Bibliography on domination in graphs and some basic definitions of domination parameters. Ibid, 257-277, 1990.

[104]    G.A. Cheston, G. Fricke, S.T. Hedetniemi, and D. P. Jacobs. On the computational complexity of upper fractional domination. ''Discrete Appl. Math.'' 27:195-207, 1990.

[105]    J. Lalani, R. Laskar and S.T. Hedetniemi. Graphs and posets: some common parameters. ''Congr. Numer.'' 71:205-216, 1990.

[106]    S.M. Hedetniemi, S.T. Hedetniemi, and D.P. Jacobs. Private domination: theory and algorithms. ''Congr. Numer.'' 79:147-157, 1990.

1991

[107]    G.S. Domke, S.T. Hedetniemi, R.C. Laskar, and G. Fricke. Relationships between integer and fractional parameters of graphs''. Proc. Sixth Quadrennial Conf. on the Theory and Applications of Graphs, Western Michigan Univ., Y. Alavi, G. Chartrand, O. Oellermann and A. Schwenk, Eds., Graph Theory, Combinatorics and Applications 1:371-387, Wiley Interscience Publ''., 1991.

[108]    A. McRae and S.T. Hedetniemi. Finding n-independent dominating sets. ''Congr. Numer.'' 85:219-234, 1991.

1993

[109]    P.J. Bernhard, S.T. Hedetniemi, and D.P. Jacobs. Efficient sets in graphs. ''Discrete Appl. Math.'' 44:99-108, 1993.

[110]    S.M. Hedetniemi, S.T. Hedetniemi and D.P. Jacobs. Total irredundance in graphs: theory and algorithms. Ars Combin. 35A:271-284, 1993.

[111]    E.J. Cockayne, B.L. Hartnell, S.T. Hedetniemi, and R. Laskar. Perfect domination in graphs, ''J. Combin. Inform. System Sci.'' 18:136-148, 1993.

1994

[112]    S. Arnborg, S. Hedetniemi and A. Proskurowski, Eds. Special Issue: Efficient Algorithms  and Partial K-trees. ''Discrete Appl. Math.'' 564(2-3):290 pp., 1994.

[113]    M. Fellows, G. Fricke, S. Hedetniemi, and D. Jacobs. The private neighbor cube. ''SIAM  J. Discrete Math.'' 7:41-47, 1994.

[114]    R. Labahn, S.T. Hedetniemi, and R. Laskar. Periodic gossiping on trees. ''Discrete Appl. Math.'' 53:235-245, 1994.

[115]    N. Chandrasekharan, S. Hedetniemi, and T. Wimer. Enumeration techniques for certain k-terminal families of graphs. ''J. Combin. Inform. System Sci.'' 19:121-138, 1994.

1995

[116]    G.H. Fricke, S.T. Hedetniemi, and M.A. Henning. Asymptotic results on distance independent domination in graphs. ''J. Combin. Inform. System Sci.'' 20:160-174, 1995.

[117]    J. Dunbar, F. Harris, S.M. Hedetniemi, S.T. Hedetniemi, R. Laskar, and A. McRae. Nearly perfect sets in graphs. Discrete Math. 138:229-246, 1995.

[118]    G.H. Fricke, S.T. Hedetniemi, and M.A. Henning. Distance independent domination in graphs. Ars Combin. 41:33-44, 1995.

[119]    E.J. Cockayne, G. Fricke, S.T. Hedetniemi, and C.M. Mynhardt. Properties of minimal dominating functions of graphs. Ars Combin. 41:107-115, 1995.

[120]    J. Dunbar, S.T. Hedetniemi, M.A. Henning, and P.J. Slater. Signed domination in graphs. In ''Proc. Seventh Quadrennial Internat. Conf. on the Theory and Applications of Graphs, Y. Alavi and A. Schwenk, Eds., Graph Theory, Combinatorics and Algorithms 1:''311-322, 1995.

[121]    G.H. Fricke, S.M. Hedetniemi, S.T. Hedetniemi, A.A. McRae, C.K. Wallis, M.S. Jacobson, H.W. Martin, and W.D. Weakley. Combinatorial problems on chessboards: a   brief survey. Ibid, 507-528, 1995.

[122]    S.M. Hedetniemi, S.T. Hedetniemi, R. Laskar, A. McRae and A. Majumdar, Domination, independence and irredundance in total graphs: a brief survey, Ibid, 671-684, 1995.

1996

[123]    J. Dunbar, S.T. Hedetniemi, M.A. Henning and A.A. McRae. Minus domination in regular graphs. Discrete Math. 149:311-312, 1996.

[124]    J. Dunbar, W. Goddard, S. Hedetniemi, A. McRae, and M.A. Henning. The algorithmic complexity of minus domination in graphs. ''Discrete Appl. Math.'' 68:73-84, 1996.

[125]    G.H. Fricke, S.T. Hedetniemi, and D.P. Jacobs. Maximal irredundant functions. ''Discrete Appl. Math.'' 68:267-277, 1996.

[126]    G.H. Fricke, S.T. Hedetniemi, D.P. Jacobs, and V. Trevisan. Reducing the adjacency matrix of a tree. Electronic J. Linear Algebra 1:34-43, 1996.

1997

[127]    J.E. Dunbar, J.W. Grossman, J.H. Hattingh, S.T. Hedetniemi, and A.A. McRae. On weakly connected domination in graphs. Discrete Math. 167/168:261-269, 1997.

[128]    J.H. Yan, G.J. Chang, S.M. Hedetniemi, and S.T. Hedetniemi. k-Path partitions in trees. ''Discrete Appl. Math.'' 78:227-233, 1997.

[129]    E.J. Cockayne, J.H. Hattingh, S.M. Hedetniemi, S.T. Hedetniemi, and A.A. McRae. Using maximality and minimality conditions to construct inequality chains. Discrete Math. 176:43-61, 1997.

[130]    S.M. Hedetniemi, S.T. Hedetniemi, and M.A. Henning. The algorithmic complexity of perfect neighborhoods in graphs. ''J. Combin. Math. Combin. Comput.'' 25:183-192, 1997.

[131]    E.J. Cockayne, P.J.P. Grobler, S.T. Hedetniemi, and A.A. McRae. What makes an irredundant set maximal? ''J. Combin. Math. Combin. Comput.'' 25:213-224, 1997.

1998

[132]    T.W. Haynes, S.T. Hedetniemi, and P.J. Slater. ''Fundamentals of Domination in Graphs. Marcel Dekker'', New York, 446 pp., 1998.

[133]    T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Eds. Domination in Graphs: Advanced  Topics. Marcel Dekker, New York, 497 pp., 1998.

[134]    S.M. Hedetniemi, S.T. Hedetniemi, and R. Reynolds. Combinatorial problems on chessboards: II, Chapter 6 in Domination in Graphs: Advanced Topics, T.W. Haynes,             S.T. Hedetniemi and P.J. Slater, Eds. Marcel Dekker, New York, 133-162, 1998.

[135]    S.T. Hedetniemi, A. A. McRae and D.A. Parks. Complexity results. Ibid, Chapter 9, 233-269, 1998.

[136]    G.H. Fricke, S.T. Hedetniemi, and D.P. Jacobs. Independence and irredundance in k-regular graphs. Ars Combin. 49:271-279, 1998.

[137]    E.J. Cockayne, S.M. Hedetniemi, S.T. Hedetniemi, and C.M. Mynhardt. Irredundant and perfect neighbourhood sets in trees. Discrete Math. 188:253-260, 1998.

[138]    I.D. Sanders and S.T. Hedetniemi. Teaching introductory computer science: a comparison of two institutions. ''Proc. 28th SACLA Conf.'', Stellenbosch, South Africa, 127-131, 1998.

1999

[139]    J. Dunbar, S. Hedetniemi, M.A. Henning, and A. McRae. Minus domination in graphs. Discrete Math.199:35-47, 1999.

[140]    G.H. Fricke, T.W. Haynes, S.M. Hedetniemi, S.T. Hedetniemi, and M.A. Henning. On perfect neighborhood sets in graphs. Discrete Math.199:221-225, 1999.

[141]    G.S. Domke, J.H. Hattingh, S.T. Hedetniemi, R.C. Laskar, and L.R. Markus. Restrained domination in graphs. Discrete Math. 203:61-69, 1999.

[1421    S.M. Hedetniemi, S.T. Hedetniemi, and D.P. Jacobs. Rank independent domination for trees. ''Bull. Inst. Combin. Appl.'' 27:62-68, 1999.

[143]    S. Hedetniemi, R. Jamison, and D. Rall. Equal unions of maximal independent sets in bipartite graphs. ''Congr. Numer.'' 141:185-190, 1999.

2000

[144]    J.E. Dunbar, S.M. Hedetniemi, S.T. Hedetniemi, D.P. Jacobs, J. Knisely, R.C. Laskar, and D.F. Rall. Fall colorings of graphs. ''J. Combin. Math. Combin. Comput.'' 33:257-273,      2000.

[145]    X. Baogen, E.J. Cockayne, T.W. Haynes, S.T. Hedetniemi, and Z. Shangchao. Extremal graphs for inequalities involving domination parameters. Discrete Math. 216:1-10, 2000.

[146]    S.M. Hedetniemi, S.T. Hedetniemi, and D.F. Rall. Acyclic domination in graphs. Discrete Math. 222:151-165, 2000.

[147]    A.M. Abdelbar, S.T. Hedetniemi, and S.M. Hedetniemi. The complexity of approximating MAPs for belief networks. J. Artificial Intelligence 124:283-288, 2000.

[148]    T.W. Haynes, S.M. Hedetniemi, and S.T. Hedetniemi. Domination and independence subdivision numbers of graphs. ''Discuss. Math. Graph Theory'' 20(2):271-280, 2000.

[149]    Grant A. Cheston, S.T. Hedetniemi, Arthur L. Liestman, and J.B. Stehman. The even adjacency split problem for graphs. ''Discrete Appl. Math.'' 102:175-188, 2000.

2001

[150]    S.T. Hedetniemi, D.P. Jacobs, and P.K. Srimani. Maximal matching stabilizes in time O(m). ''Inform. Process. Lett.'' 80:221-223, 2001.

[151]    T.W. Haynes, S.M. Hedetniemi, S.T. Hedetniemi, D.P. Jacobs, J. Knisely, and L.C. van der Merwe. Domination subdivision numbers. ''Discuss. Math. Graph Theory'' 21(2):239-         253, 2001.

[152]    T.W. Haynes, S.T. Hedetniemi, M.A. Henning, and D.J. Knisley. Stable and unstable graphs with total irredundance number zero. Ars Combin. 61:33-46, 2001.

[153]    J.R.S. Blair, S.M. Hedetniemi, S.T. Hedetniemi, and D.P. Jacobs. Self-stabilizing maximum matchings. ''Congr. Numer.'' 153:151-159, 2001.

2002

[154]    G.H. Fricke, T.W. Haynes, S.M. Hedetniemi, S.T. Hedetniemi, and R.C. Laskar. Excellent trees. ''Bull. ICA'' 34:27-38, 2002.

[155]    O. Favaron, S.M. Hedetniemi, S.T. Hedetniemi, and D.F. Rall. On k-dependent domination. Discrete Math. 249:83-94, 2002.

[156]    T.W. Haynes, S.M. Hedetniemi, S.T. Hedetniemi, and M.A. Henning. Power domination  in graphs applied to electrical power networks. SIAM J. Discrete Math. 15(4):519-529, 2002.

[157]    O. Favaron, T. Haynes, S.T. Hedetniemi, M.A. Henning, and D. Knisley. Total irredundance in graphs. Discrete Math. 256:115-127, 2002.

[158]    S.T. Hedetniemi, D.P. Jacobs, and P.K. Srimani. Fault tolerant distributed coloring algorithms that stabilize in linear time. ''Proc. IEEE IPDPS-2002 Workshop on Advances          in Parallel and Distributed Computational Models'', Orlando, FL, 1-5, 2002.

[159]    O. Favaron, G. Fricke, W. Goddard, S.M. Hedetniemi, S.T. Hedetniemi, P. Kristiansen, R.C. Laskar, and D. Skaggs. Offensive alliances in graphs, ''Proc. 17th Internat. Symp. Comput. Inform. Sci.'',I. Cicekli, N.K. Cicekli and E. Gelenbe, Eds., ISCIS, Orlando, FL,     CRC Press,  298-302, 2002.

[160]    T.W. Haynes, S.T. Hedetniemi, and M.A. Henning. Global defensive alliances. Ibid,  303-307, 2002.

[161]    P. Kristiansen, S.M. Hedetniemi, and S.T. Hedetniemi. Introduction to alliances in graphs. Ibid, 308-312, 2002.

[162]    S. Balasubramanian, J. Farr, K. Bernasconi, R. Laskar, J. Villalpando, K. Hutson, G. Stevens, M. Gairing, and S.T. Hedetniemi. Gallai theorems involving domination             parameters. ''Congr. Numer.'' 157:149-157, 2002.

2003

[163]    T.W. Haynes, S.T. Hedetniemi, M.A. Henning, and P.J. Slater. H-forming sets in graphs. Discrete Math. 262:159-169, 2003.

[164]    T.W. Haynes, S.T. Hedetniemi, and L.C. van der Merwe. Total domination subdivision numbers. ''J. Combin. Math. Combin. Comput.'' 44:115-128, 2003.

[165]    G.H. Fricke, L.M. Lawson, T.W. Haynes, S.M. Hedetniemi, and S.T. Hedetniemi. A note on defensive alliances in graphs. ''Bull. ICA'' 38:37-41, 2003.

[166]    M.A. Henning and S.T. Hedetniemi. Defending the Roman Empire - A new strategy. Discrete Math. 266:239-251, 2003.

[167]    S.T. Hedetniemi, D.P. Jacobs, and P.K. Srimani. Linear time self-stabilizing colorings. I''nform. Process. Lett.'' 87:251-255, 2003.

[168]    P. Erdös, S.T. Hedetniemi, R.C. Laskar, and G. Prins. On the equality of the partial Grundy and upper ochromatic numbers of graphs. Discrete Math. 272:53-64, 2003.

[169]    S.M. Hedetniemi, S.T. Hedetniemi, D.P. Jacobs, and P.K. Srimani. Self-stabilizing algorithms for minimal dominating sets and maximal independent sets. ''Comput. Math. Appl.'' 46:803-811, 2003.

[170]    T.W. Haynes, S.T. Hedetniemi, and M.A. Henning. Global defensive alliances in graphs. Electronic J. Combin.10(1):R47, Dec 8, 2003.

[171]    M. Gairing, S.T. Hedetniemi, P. Kristiansen, and A.A. McRae. Self-stabilizing algorithms for {k}-domination. ''Proc. Sixth Symp. on Self-Stabilization (SSS 2003), San Francisco, CA, Springer-Verlag LNCS'' 2074:49-60, 2003.

[172]    W. Goddard, S.T. Hedetniemi, D.P. Jacobs, and P.K. Srimani. A self-stabilizing distributed algorithm for minimal total domination in an arbitrary system graph. ''Proc. Eighth IPDPS Workshop on Formal Methods for Parallel Programming: Theory and Applications'', Nice, France, April 22-26, 2003.

[173]    W. Goddard, S.T. Hedetniemi, D.P. Jacobs, and P.K. Srimani. Self-stabilizing protocols for maximal matching and maximal independent sets for ad hoc networks, ''Proc. Fifth        IPDPS Workshop on Advances in Parallel and Distributed Computational   Models'', Nice, France, April 22-26, 2003.

[174]    W. Goddard, S.T. Hedetniemi, D.P. Jacobs, and P.K. Srimani. A robust distributed generalized matching protocol that stabilizes in linear time. ''Proc. ICDCS Internat. Workshop on Mobile Distributed Computing (MDC03)'', Rhode Island, May 19-22, 2003.

[175]    W. Goddard, S.T. Hedetniemi, D.P. Jacobs, and P.K. Srimani. Self-stabilizing distributed algorithm for strong matching in a system graph. In HiPC 2003, T.M. Pinkston and V.K. Prasanna, Eds, Springer-Verlag, LNCS 2913:66-73, 2003.

[176]    Z. Xu, S.T. Hedetniemi, W. Goddard, and P.K. Srimani. A synchronous self-stabilizing minimal dominating protocol in an arbitrary network graph''. Proc. 5th Internat. Workshop        on Distributed Computing (IWDC2003),  LNCS'' 2918:26-32, 2003.

2004

[177]    K.B. Reid, A.A. McRae, S.M. Hedetniemi, and S.T. Hedetniemi. Domination and irredundance in tournaments. Australasian  J. Combin. 29:157-172, 2004.

[178]    E.J. Cockayne, P.A. Dreyer, Jr., S.M. Hedetniemi, and S.T. Hedetniemi. Roman domination in graphs. Discrete Math. 278:11-22, 2004.

[179]    S.M. Hedetniemi, S.T. Hedetniemi, and P. Kristiansen. Alliances in graphs. ''J. Combin. Math. Combin. Comput.'' 48:157-177, 2004.

[180]    M. Gairing, W. Goddard, S.T. Hedetniemi, and D.P. Jacobs. Self-stabilizing maximal k-dependent sets in linear time. ''Parallel Process. Lett''. 14(1):75-82, 2004.

[181]    Z. Shi, W. Goddard, and S.T. Hedetniemi. An anonymous self-stabilizing algorithm for 1-maximal independent set in trees. ''Inform. Process. Lett''. 91:77-83, 2004.

[182]    S.M. Hedetniemi, S.T. Hedetniemi, A.A. McRae, D. Parks, and J.A. Telle. Iterated colorings of graphs. Discrete Math. 278:81-104, 2004.

[183]    M. Gairing, R.E. Geist, S.T. Hedetniemi, and P. Kristiansen. A self-stabilizing algorithm for maximal 2-packing. Nordic J. Comput. 11(1):1-11, 2004.

[184]    O. Favaron, T.W. Haynes, and S.T. Hedetniemi. Domination subdivision numbers in graphs, ''Util. Math.'' 66:195-209, 2004.

[185]    O. Favaron, G. Fricke, W. Goddard, S.M. Hedetniemi, S.T. Hedetniemi, P. Kristiansen, R.C. Laskar, and R.D. Skaggs. Offensive alliances in graphs. ''Discuss. Math. Graph Theory'' 24:263-275, 2004.

[186]    T.W. Haynes, S.T. Hedetniemi, and M.A. Henning. A characterization of trees with equal domination and global strong alliance numbers. ''Util. Math.'' 66:105-119, 2004.

[187]    W. Goddard, S.T. Hedetniemi, D.P. Jacobs, and P.K. Srimani. Fault tolerant algorithms for orderings and colorings''. Proc. IPDPS Workshop on Advances in Parallel and       Distributed Computational Models (APDCM04),'' Santa Fe, New Mexico, April, 2004.

[188]    R.C. Brigham, R.D. Dutton, and S.T. Hedetniemi. A sharp lower bound on the powerful alliance number of Cm x Cn, ''Congr. Numer.'' 167:57-63, 2004.

[189]    M. Gairing, W. Goddard, S.T. Hedetniemi, P. Kristiansen and A.A. McRae, Distance-two information in self-stabilizing algorithms, ''Parallel Process. Lett''. 14:387-398, 2004.

2005

[190]    W. Goddard, S.M. Hedetniemi, and S.T. Hedetniemi. Eternal security in graphs. ''J. Combin. Math. Combin. Comput.'' 52:169-180, 2005.

[191]    W. Goddard, S.T. Hedetniemi, D.P. Jacobs, and P.K. Srimani. Self-stabilizing algorithms for orderings and colorings'', Int. J. Found. Comput. Sci.'' 16(1):19-36, 2005.

[192]    W. Goddard, S.M. Hedetniemi, S.T. Hedetniemi, and R. Laskar. Generalized subgraph-restricted matchings in graphs. Discrete Math. 293:129-138, 2005.

[193]    J.E. Dunbar, T.W. Haynes, and S.T. Hedetniemi. Nordhaus-Gaddum bounds for domination sums in graphs with specified minimum degree. ''Util. Math.'' 67:97-105, 2005.

[194]    W. Goddard, S.T. Hedetniemi, D.P. Jacobs, and P.K. Srimani. Self-stabilizing global optimization algorithms for large network graphs''. Internat. J. Dist. Sensor Networks''             1:329-344, 2005.

[195]    Z. Shi, W. Goddard, S.T. Hedetniemi, K. Kennedy, R. Laskar, and A. McRae. An algorithm for partial Grundy number on trees. Discrete Math. 304:108-116, 2005.

[196]     J.R.S. Blair, W. Goddard, S.M. Hedetniemi, S.T. Hedetniemi and S.B. Horton, Domination equivalence in graphs, ''AKCE Internat. J. Graphs Combin.'' 2(2):123-136, 2005.

2006

[197]    J.E. Dunbar, D.J. Erwin, T.W. Haynes, S.M. Hedetniemi, and S.T. Hedetniemi. Broadcasts in graphs. ''Discrete Appl. Math.'' 154(1):59-75, 2006.

[198]    T.W. Haynes, S.M. Hedetniemi, S.T. Hedetniemi, J.R. Lewis and P.J. Slater,  Differentials in graphs, ''Util. Math''. 69:43-54, 2006.

[199]   S.T. Hedetniemi. Unsolved algorithmic problems on trees. AKCE Internat. 3:1-37, 2006.

[200]   W. Goddard, S. Hedetniemi, D. Jacobs and V. Trevisan. Distance-k information in self-stabilizing algorithms. 13th Colloquium on Structural Information and Communication            Complexity (SIROCCO), (Chester, UK, 2006), LNCS 4056:349-356, 2006.

[201]    G.H. Fricke, S.T. Hedetniemi and D.P. Jacobs. On the equivalence of the upper irredundance and fractional upper irredundance numbers in graphs''. Bull ICA'' 48:99-106,      2006.

[202]    W. Goddard, S.T. Hedetniemi and Z. Shi, An anonymous self-stabilizing algorithm for 1- maximal matching in trees. Proceedings of the 2006 Internat. Conf. on Parallel and             Distributed Processing Techniques and Applications (PDPTA’06), Las Vegas, USA, Vol. II, 2006, 797-803.

2007

[203]    R.C. Brigham, R.D. Dutton and S.T. Hedetniemi, Security in graphs, ''Discrete Appl. Math''. 155:1708-1714, 2007.

2008

[204]    W. Goddard, S.T. Hedetniemi, D.P. Jacobs, and P.K. Srimani, Anonymous daemon conversion in self-stabilizing algorithms by randomization in constant space, ICDCN             2008, LNCS 4904:182-190, 2008.

[205]    J.R.S. Blair, W. Goddard, S.T. Hedetniemi, S. Horton, P. Jones and G. Kubicki, On domination and reinforcement numbers in trees, Discrete Math. 308:1165-1175, 2008.

[206]    W. Goddard, S.T. Hedetniemi, D.P. Jacobs, P.K. Srimani and Z. Xu, Self-stabilizing graph protocols, ''Parallel Process. Lett.'', 18(1):189-199, 2008.

[207]    W. Goddard, S.T. Hedetniemi, D.P. Jacobs and V. Trevisan, Distance-$k$ knowledge in self-stabilizing algorithms, ''Theoretical Comput. Sci''.,399:118-127, 2008.

[208]   W. Goddard, S.M. Hedetniemi, S.T. Hedetniemi J.M. Harris and D.F. Rall, Broadcast chromatic numbers of graphs, ''Ars Combin. 86:33-49, 2008''.

[209]    T.W. Haynes, S.M. Hedetniemi, S.T. Hedetniemi, A.A. McRae and P.J. Slater, Irredundant colorings of graphs, ''Bull. ICA'' 54:93-121, 2008.

[210]    S.M. Hedetniemi, S.T. Hedetniemi, J. Knisely, and D.F. Rall, Secondary domination in graphs, ''AKCE Internat. J. Graphs and Combinatorics,'' 5(2):103-115, 2008.

[211]    A.C. Jamieson, W. Goddard and S.T. Hedetniemi, On the Wimer method for designing edge-based algorithms, ''AKCE Internat. J. Graphs and Combinatorics'', 5(2): 117-125, 2008.

[212]    S.M. Hedetniemi, S.T. Hedetniemi, R.C. Laskar, L. Markus and P.J. Slater, Disjoint dominating sets in graphs, ''Proc. of Internat. Conf. Discrete Math., ICDM 2006, 7:87-100, Ramanujan Math.Soc., Lecture Notes Series No. 7 in Discrete Mathematics'', 2008.

2009

[213]   J. Dabney, B.C. Dean and S.T. Hedetniemi, A linear-time algorithm for broadcast domination in a tree, Networks 53(2): 160-169, 2009.

[214]   W. Goddard and S.T. Hedetniemi, A note on trees, tables and algorithms. Networks 53(2):184-190, 2009.

[215]   J. T. Hedetniemi, K. D. Hedetniemi, S. M. Hedetniemi, and S. T. Hedetniemi, Secondary and internal distances of sets in graphs, ''AKCE Int. J. Graphs Combin. 6(2):239-266, 2009.''