Biclique coverings of regular bigraphs and minimum semiring ranks of regular matrices

• Published in: Journal of combinatorial theory. Series B Vol. 51; no. 1; pp. 73 - 89
• Main Authors: Gregory, David A, Pullman, Norman J, Jones, Kathryn F, Lundgren, J.Richard
• Format: Journal Article
• Language: English
• Published: Duluth, MN Elsevier Inc 1991; Academic Press
• Subjects: Combinatorics; Combinatorics. Ordered structures; Exact sciences and technology; Graph theory; Mathematics; Sciences and techniques of general use; Partition; Bipartite graph; Graph covering; Square matrix; Regular graph; Extremum problem

We study the minimum number of complete bipartite subgraphs needed to cover and partition the edges of a k-regular bigraph on 2 n vertices. Bounds are determined on the minima of these numbers for fixed n and k. Exact values of the minima are found for all n and k ≤ 4. The same results hold for dire...