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TR12-039 | 17th April 2012 13:01
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#### Clique Problem, Cutting Plane Proofs, and Communication Complexity

**Abstract:**
Motivated by its relation to the length of cutting plane proofs for the Maximum Biclique problem, here we consider the following communication game on a given graph G, known to both players. Let K be the maximal number of vertices in a complete bipartite subgraph of G (which is not necessarily an induced subgraph if G is not bipartite). Alice gets a set A of vertices, and Bob gets a disjoint set B of vertices such that |A|+|B|>K. The goal is to find a nonedge of G between A and B. We show that O(\log n) bits of communication are enough for every n-vertex graph.