Clique problem, cutting plane proofs and communication complexity

Computer Science – Computational Complexity

Scientific paper

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10 pages. Theorem 1 in the previous version holds only for bipartite graphs, the non-bipartite case remains open. I now separa

Scientific paper

Motivated by its relation to the length of cutting plane proofs for the Maximum Biclique problem, 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.

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