Maximum Edge Bicliques in Tree Convex Bipartite Graphs

We show that the computational complexity of the maximum edge biclique (MEB) problem in tree convex bipartite graphs depends on the associated trees. That is, MEB is \(\mathcal {NP}\)-complete for star convex bipartite graphs, but polynomial time solvable for tree convex bipartite graphs whose associated trees have a constant number of leaves. In particular, MEB is polynomial time solvable for triad convex bipartite graphs. Moreover, we show that the same algorithm strategy may not work for circular convex bipartite graphs, and triad convex bipartite graphs are incomparable with respect to chordal bipartite graphs.