Fractional Biclique Covers and Partitions of Graphs

A biclique is a complete bipartite subgraph of a graph. This paper investigates the fractional biclique cover number, bc(G), and the fractional biclique partition number, bp(G), of a graph G. It is observed that bc(G) and bp(G) provide lower bounds on the biclique cover and partition numbers respectively, and conditions for equality are given. It is also shown that bc(G) is a better lower bound on the Boolean rank of a binary matrix than the maximum number of isolated ones of the matrix. In addition, it is noted that bc(G) bp(G) (G), the fractional vertex cover number. Finally, the application of bc(G) and bp(G) to two different weak products is discussed.

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Valerie L. Watts
• Keywords: COMBINATORICS 2006, Fractional Biclique, Lower Bound, Partition Numbers