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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 ...
For a graph G, let χ(G) denote the chromatic number and Δ(G) the maximum degree of G.The list coloring number ch(G) satisfies the following properties.. ch(G) ≥ χ(G).A k-list-colorable graph must in particular have a list coloring when every vertex is assigned the same list of k colors, which corresponds to a usual k-coloring.
The discharging method is a technique used to prove lemmas in structural graph theory. [1] Discharging is most well known for its central role in the proof of the four color theorem. The discharging method is used to prove that every graph in a certain class contains some subgraph from a specified list.
The "pearls" of the title include theorems, proofs, problems, and examples in graph theory.The book has ten chapters; after an introductory chapter on basic definitions, the remaining chapters material on graph coloring; Hamiltonian cycles and Euler tours; extremal graph theory; subgraph counting problems including connections to permutations, derangements, and Cayley's formula; graph ...
Concise, annotated list of graph theory resources for researchers; rocs — a graph theory IDE; The Social Life of Routers — non-technical paper discussing graphs of people and computers; Graph Theory Software — tools to teach and learn graph theory; Online books, and library resources in your library and in other libraries about graph theory
In 2003, Carsten Thomassen [3] derived an alternative proof from another related theorem: every planar graph with girth at least five is 3-list-colorable. However, Grötzsch's theorem itself does not extend from coloring to list coloring: there exist triangle-free planar graphs that are not 3-list-colorable. [ 4 ]
Example of Hedetniemi's conjecture: the tensor product of C5 and C3 (on the left) produces a graph that contains a cycle with length 15 (on the right) so: the resulting graph requires 3 colors. In graph theory , Hedetniemi's conjecture , formulated by Stephen T. Hedetniemi in 1966, concerns the connection between graph coloring and the tensor ...
Induction step for proof of Fáry's theorem. One way of proving Fáry's theorem is to use mathematical induction. [1] Let G be a simple plane graph with n vertices; we may add edges if necessary so that G is a maximally plane graph. If n < 3, the result is trivial.