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arXiv · 1405.1974

Computing the partition function for cliques in a graph

Alexander Barvinok
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Abstract

We present a deterministic algorithm which, given a graph G with n vertices and an integer 1 0 is an absolute constant: we can choose gamma=0.06, and if n > 4m and m > 10, we can choose gamma=0.18. This allows us to tell apart the graphs that do not have m-subsets of high density from the graphs that have sufficiently many m-subsets of high density, even when the probability to hit such a subset at random is exponentially small in m.

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Alexander Barvinok. 2014-10-13. Computing the partition function for cliques in a graph. https://arxiv.org/abs/1405.1974

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