Finding biclique partitions of co-chordal graphs

The biclique partition number (bp) of a graph G is referred to as the least complete bipartite (biclique) subgraphs that are required cover edges exactly once. In this paper, we show co-chordal (complementary chordal) G=(V,E) less than maximal cliques (mc) its complementary graph: A chordal Gc=(V,Ec). We first provide general framework “divide and conquer” heuristic finding minimum partitions graphs based on clique trees. Furthermore, complexity O(|V|(|V|+|Ec|)) proposed by applying lexicographic breadth-first search find structures called moplexes. Either gives us with size mc(Gc)−1. addition, prove both our heuristics can solve problem if complement Gc vertex irreducible. also mc(Gc)−2≤bp(G)≤mc(Gc)−1 split graph.