A New Spectral Bound on the Clique Number of Graphs

Many computer vision and patter recognition problems are intimately related to the maximum clique problem. Due to the intractability of this problem, besides the development of heuristics, a research direction consists in trying to find good bounds on the clique number of graphs. This paper introduces a new spectral upper bound on the clique number of graphs, which is obtained by exploiting an invariance of a continuous characterization of the clique number of graphs introduced by Motzkin and Straus. Experimental results on random graphs show the superiority of our bounds over the standard literature. © 2010 Springer-Verlag Berlin Heidelberg.