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Finding the chromatic number by means of critical graphs
2000
Electronic Notes in Discrete Mathematics
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-graphs 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.
doi:10.1016/s1571-0653(05)80155-6
fatcat:oylwxhacqng4haq52yzkkydrn4