Finding the chromatic number by means of critical graphs

Francine Herrmann, Alain Hertz
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.
more » ... experiments on random graphs and on DIMACS benchmark problems demonstrate that the new proposed algorithm can solve larger problems than previous known exact methods.
doi:10.1016/s1571-0653(05)80155-6 fatcat:oylwxhacqng4haq52yzkkydrn4