We propose a new exact algorithm for finding the chromatic number of a graph
G
. The algorithm attempts to determine the smallest possible induced subgraph
G'
of
G
which has the same chromatic number as
G
. Such a subgraph is said critical since all proper induced sub-graph of
G'
have a chromatic number strictly smaller than
G'
.The proposed method is particularly helpful when a
k
-coloring of a non-critical graph is known, and it has to be proved that no (
k
-1)-coloring of
G
exists. Computational experiments on random graphs and on DIMACS benchmark problems demonstate that the new proposed algorithm can solve larger problem than previous known exact methods.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.