Clique Problem, Cutting Plane Proofs and Communication

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 with maximum bipartite clique size K. Two parties separately receive disjoint subsets A,B of vertices such that |A | + |B |> K. The goal is to identify a nonedge between A and B. We prove that O(logn) bits of communication are enough for any n-vertex graph