A note on \(d\)-biclique covers (Q2831584)

The minimum number of complete bipartite subgraphs that cover all edges of a graph \(G\) is denoted by bc\((G)\). Here a generalized version of this setting is considered, where each edge is to be covered at least \(d\) times; the corresponding invariant is then denoted by bc\(_{d}(G)\). Bounds and exact values for bc\(_{d}(G)\) are obtained for various constructions, including the lexicographic product of graphs, the join of graphs, and the Mycielski graph of graphs.