Assertion: graph's number | /r/HasProperty | chromatic
Facets:
Source sentences:
text: By Brooks' theorem, any graph other than a clique or an odd cycle has chromatic number at most Δ, and by Vizing's theorem any graph has chromatic index at most Δ + 1.
text: The smallest number of colors needed for an edge coloring of a graph G is the chromatic index, or edge chromatic number, χ′(G).
text: The smallest number of colors needed to color a graph G is called its chromatic number, and is often denoted χ(G).
text: For any positive integers g and χ, there exists a graph with girth at least g and chromatic number at least χ; for instance, the Grötzsch graph is triangle-free and has chromatic number 4, and repeating the Mycielskian construction used to form the Grötzsch graph produces triangle-free graphs of arbitrarily large chromatic number.
text: A k-degenerate graph has chromatic number at most k + 1; this is proved by a simple induction on the number of vertices which is exactly like the proof of the six-color theorem for planar graphs.