Strong Biclique Cover of Planar Graphs

A t-strong biclique cover of a graph G is an edge cover, E(G) =⋃ti =1E(Hi), where each Hi is a set of disjoint bicliques (complete bipartite graphs), say Hi1, …. ,Hiri , such that for any 1≤ j ≤ k≤ ri, the graph G has no edges between Hik and Hij . The strong biclique cover number S(G) is the minimum number t for which there exists a t-strong biclique cover of G. In this paper, we investigate the strong biclique cover number of graphs. We show that the strong biclique cover number of planar graphs is a constant number.