Comparison between the maximum clique and maximum biclique problem It seems to be commonly believed that the maximum biclique problem (on a bipartite graph) is more difficult than the original maximum clique problem. Is there a formal proof for this claim? (For example, a reduction of the maximum clique problem to the maximum biclique problem.)
Besides the recent W(1)-hardness result for the parametrized complexity of the biclique problem (pointed out by R B), here is a paper whose abstract gives some detailed information about the polynomial-time solvability of variants of biclique detection.