The study of graph colouring has long been a central topic in discrete mathematics, with a prominent focus on optimising the assignment of labels or colours to vertices such that adjacent vertices are ...

Abstract: The b-chromatic number of a graph, written as φ(G), is the highest number of colors you can use to color the graph properly, with one special rule: in each color group, there must be at ...

A collection of algorithms for calculating the chromatic number of undirected graphs, including Brute Force, Greedy, DSatur, Backtracking, RLF, 3-SAT, and DFS.

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Vol. 12, No. 4, Dedicated to Professor Ko-Wei Lih on the Occasion of His 60th Birthday (July 2008), pp. 997-1005 (9 pages) The circular chromatic number χc(G) of a graph G is a very natural ...

We derive a formula for the chromatic polynomial of a chordal or a triangulated graph in terms of its maximal cliques. As a corollary we obtain a way to write down an explicit formula for the ...