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d-defective chromatic number

The minimum number of colours k required for which G is (k, d)-colourable is called the d-defective chromatic number, χ d ( G ) {\displaystyle \chi _{d}(G)} {\displaystyle \chi _{d}(G)}.[10]

For a graph class G, the defective chromatic number of G is minimum integer k such that for some integer d, every graph in G is (k,d)-colourable. For example, the defective chromatic number of the class of planar graphs equals 3, since every planar graph is (3,2).colourable as stated above.

Robert Cowen