The Monotone Complexity of k-clique on Random Graphs

SIAM J. Comput., pp. 256-279, 2014.

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random graphsmonotone complexitys-rado sunflower lemmahigh probabilityaverage-case hardness resultMore(20+)

Abstract:

It is widely suspected that Erd\H{o}s-R\'enyi random graphs are a source of hard instances for clique problems. Giving further evidence for this belief, we prove the first average-case hardness result for the $k$-clique problem on monotone circuits. Specifically, we show that no monotone circuit of size $O(n^{k/4})$ solves the $k$-clique ...More

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