List of graph theory topics

This is a list of graph theory topics, by Wikipedia page.

See glossary of graph theory terms for basic terminology

Examples and types of graphs
• Amalgamation

• Bipartite graph

• * Complete bipartite graph

• * Disperser

• * Expander

• * Extractor

• Bivariegated graph

• Cage (graph theory)

• Cayley graph

• Circle graph

• Clique graph

• Cograph

• Common graph

• Complement of a graph

• Complete graph

• Cubic graph

• Cycle graph

• De Bruijn graph

• Dense graph

• Dipole graph

• Directed acyclic graph

• Directed graph

• Distance regular graph

• Distance-transitive graph

• Edge-transitive graph

• Interval graph

• Interval graph, improper

• Interval graph, proper

• Line graph

• Lollipop graph

• Minor

• * Robertson–Seymour theorem

• Petersen graph

• Planar graph

• * Dual polyhedron

• * Outerplanar graph

• Random graph

• Regular graph

• Scale-free network

• Snark (graph theory)

• Sparse graph

• * Sparse graph code

• Split graph

• String graph

• Strongly regular graph

• Threshold graph

• Total graph

• Tree (graph theory).

• Trellis (graph)

• Turán graph

• Ultrahomogeneous graph

• Vertex-transitive graph

• Visibility graph

• * Museum guard problem

• Wheel graph

Graph coloring
• Acyclic coloring

• Chromatic polynomial

• Cocoloring

• Complete coloring

• Edge coloring

• Exact coloring

• Four color theorem

• Fractional coloring

• Goldberg–Seymour conjecture

• Graph coloring game

• Graph two-coloring

• Harmonious coloring

• Incidence coloring

• List coloring

• List edge-coloring

• Perfect graph

• Ramsey's theorem

• Sperner's lemma

• Strong coloring

• Subcoloring

• Tait's conjecture

• Total coloring

• Uniquely colorable graph

Paths and cycles
• Path (graph theory)

• Seven Bridges of Königsberg

• * Eulerian path

• Three-cottage problem

• Shortest path problem

• * Dijkstra's algorithm

• ** Open Shortest Path First

• Flooding algorithm

• Route inspection problem

• Hamiltonian path

• * Hamiltonian path problem

• * Knight's tour

• Traveling salesman problem

• * Nearest neighbour algorithm

• * Bottleneck traveling salesman problem

• Path analysis (paths and cycles)

Trees
• Abstract syntax tree

• B-tree

• Binary tree

• *Binary search tree

• **Self-balancing binary search tree

• ***AVL tree

• ***Red–black tree

• ***Splay tree

• ***T-tree

• *Binary space partitioning

• *Full binary tree

• B*-tree

• Heap

• *Binary heap

• *Binomial heap

• *Fibonacci heap

• *2-3 heap

• Kd-tree

• Cover tree

• Decision tree

• Empty tree

• Evolutionary tree

• Exponential tree

• Family tree

• Fault tree

• Free tree

• Game tree

• K-ary tree

• Octree

• Parse tree

• Phylogenetic tree

• Polytree

• Positional tree

• PQ tree

• R-tree

• Rooted tree

• *Ordered tree

• *Recursive tree

• SPQR tree

• Suffix tree

• Technology tree

• Trie

• *Patricia trie

• Spanning tree

• *Minimum spanning tree

• **Boruvka's algorithm

• **Kruskal's algorithm

• **Prim's algorithm

• Steiner tree

• Quadtree

Terminology

 * Node
 * Child node
 * Parent node
 * Leaf node
 * Root node
 * Root (graph theory)

Operations
• Tree rotation

• Tree traversal

• *Inorder traversal

• *Backward inorder traversal

• *Pre-order traversal

• *Post-order traversal

• *Ahnentafel

• Tree search algorithm

• A-star search algorithm

• Best-first search

• Breadth-first search

• Depth-first search

• *Iterative deepening depth-first search


 * Tree structure
 * Tree data structure
 * Cayley's formula
 * Kőnig's lemma
 * Tree (set theory) (need not be a tree in the graph-theory sense, because there may not be a unique path between two vertices)
 * Tree (descriptive set theory)
 * Euler tour technique

Graph limits

 * Graphon

Graphs in logic

 * Conceptual graph
 * Entitative graph
 * Existential graph
 * Laws of Form
 * Logical graph

Mazes and labyrinths

 * Labyrinth
 * Maze
 * Maze generation algorithm

Algorithms

 * Ant colony algorithm
 * Breadth-first search
 * Depth-first search
 * Depth-limited search
 * FKT algorithm
 * Flood fill
 * Graph exploration algorithm
 * Matching (graph theory)
 * Max flow min cut theorem
 * Maximum-cardinality search
 * Shortest path
 * Dijkstra's algorithm
 * Bellman–Ford algorithm
 * A* algorithm
 * Floyd–Warshall algorithm
 * Topological sorting
 * Pre-topological order

Other topics
• Adjacency list

• Adjacency matrix

• *Adjacency algebra – the algebra of polynomials in the adjacency matrix

• Canadian traveller problem

• Cliques and independent sets

• *Clique problem

• Connected component

• Cycle space

• de Bruijn sequences

• Degree diameter problem

• Entanglement (graph measure)

• Erdős–Gyárfás conjecture

• Eternal dominating set

• Extremal graph theory

• *Critical graph

• *Turán's theorem

• Frequency partition

• Frucht's theorem

• Girth

• Graph drawing

• Graph homomorphism

• Graph labeling

• *Graceful labeling

• Graph partition

• Graph pebbling

• Graph property

• Graph reduction

• Graph-structured stack

• Graphical model

• *Bayesian network

• *D-separation

• *Markov random field

• Tree decomposition (Junction tree) and treewidth

• Graph triangulation (see also Chordal graph)

• Perfect order

• Hidden Markov model

• *Baum–Welch algorithm

• *Viterbi algorithm

• Incidence matrix

• Independent set problem

• Knowledge representation

• *Conceptual graph

• *Mind map

• Level structure

• Link popularity

• Mac Lane's planarity criterion

• Node influence metric

• Reconstruction conjecture

• Scientific classification

• *Cladistics

• *Neighbor-joining

• *Phenetics

• Turán number

• Shannon switching game

• Spectral graph theory

• Spring-based algorithm

• Strongly connected component

• Vertex cover problem

Networks, network theory
See list of network theory topics

Hypergraphs

 * Helly family
 * Intersection (Line) Graphs of hypergraphs