Strong Biclique Cover of Planar Graphs

‎A $t$-{\it strong biclique cover} of a graph $G$ is an edge cover‎, ‎$E(G) = \cup_{i=1}^t‎ ‎E(H_i)$‎, ‎where each $H_i$ is a set of disjoint bicliques (complete bipartite graphs)‎, ‎say $H_{i1}‎, ‎\ldots‎ ‎,H_{ir_i}$,‎ ‎such that for any $1 \leq j k \leq r_i$‎, ‎the graph $G$ has no edges between $H_{ik}$ and $H_{ij}$‎. ‎The {\it 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