Improved Infra-Chromatic Bound for Exact Maximum Clique Search
This paper improves an infra-chromatic bound which is used by the exact branch-and-bound maximum clique solver BBMCX (San Segundo et al., 2015, Computers & Operations Research, p. 293-303) as an upper bound on the clique number for every subproblem. The infra-chromatic bound looks for triplets of color subsets which cannot contain a 3-clique. As a result, it is tighter than the bound obtained by widely used approximate-coloring algorithms because it can be lower than the chromatic number. The reported results show that our algorithm with the new bound significantly outperforms the state-of-the-art algorithms in a number of structured and uniform random graphs.