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!