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

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...

Full description

Saved in:
Bibliographic Details
Published inJournal 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
LanguageEnglish
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
Online AccessGet full text

Cover

More Information
Summary: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 directed graphs. Equivalently, we have determined bounds on the minimum value of the Boolean and nonnegative integer ranks of binary n × n matrices with constant row and column sum k for fixed n and k, obtaining the exact values of the minimum for k ≤ 4.
ISSN:0095-8956
1096-0902
DOI:10.1016/0095-8956(91)90006-6