We examine a bipartite graph with two sides $R$ and $L$. We know only that each node on side $R$ is connected to $k$ nodes on side $L$, and that $|R| \ll k< |L|$ (where $|L|$ and $|R|$ denote the number of nodes in each side, and $\ll$ denotes "much larger than").

What is the minimal size (i.e., number of edges) of the maximal biclique$^1$?

(1) Maximal biclique: A complete bipartite subgraph, that isn't a subgraph of another complete bipartite subgraph.