# A good upper bound on the size of k-biclique in random bipartite graphs.

Let $G = (X \cup Y, E)$ be a random bipartite graph, where $X$ and $Y$ are the set of vertices and $E$ the set of edges. I want to find an upper bound of the largest biclique in which exactly $k$ vertices of $X$ are part of the biclique. A biclique of $G$ is a set of vertices $X' \subset X$ and $Y' \subset Y$ where there is a edge between each node $x \in X'$ and each node $y \in Y'$. Could any of you help me on this? Thanks!

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This is very elementary. Is it homework? –  Brendan McKay Dec 29 '12 at 1:28
No. I know some upper bounds.. but i need an algorithm to find a strong one, since i'm using it to write a branch-and-bound algorithm to solve the problem. –  totheend Dec 29 '12 at 12:03