Half-regular factorizations of the complete bipartite graph

Mark Aksen, I. Miklós, Kathleen Zhou

Research output: Contribution to journalArticle

Abstract

We consider a bipartite version of the color degree matrix problem. A bipartite graph G(U,V,E) is half-regular if all vertices in U have the same degree. We give necessary and sufficient conditions for a bipartite degree matrix (also known as demand matrix) to be the color degree matrix of an edge-disjoint union of half-regular graphs. We also give necessary and sufficient perturbations to transform realizations of a half-regular degree matrix into each other. Based on these perturbations, a Markov chain Monte Carlo method is designed in which the inverse of the acceptance ratios is polynomial bounded. Realizations of a half-regular degree matrix are generalizations of Latin squares, and they also appear in applied neuroscience.

Original languageEnglish
Pages (from-to)21-33
Number of pages13
JournalDiscrete Applied Mathematics
Volume230
DOIs
Publication statusPublished - Oct 30 2017

Fingerprint

Complete Bipartite Graph
Factorization
Color
Perturbation
Neuroscience
Magic square
Markov Chain Monte Carlo Methods
Regular Graph
Bipartite Graph
Markov processes
Disjoint
Union
Monte Carlo methods
Polynomials
Transform
Sufficient
Necessary Conditions
Polynomial
Necessary
Sufficient Conditions

Keywords

  • Degree matrix
  • Degree sequences
  • Edge packing
  • Graph factorization
  • Latin squares
  • Markov chain Monte Carlo

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Half-regular factorizations of the complete bipartite graph. / Aksen, Mark; Miklós, I.; Zhou, Kathleen.

In: Discrete Applied Mathematics, Vol. 230, 30.10.2017, p. 21-33.

Research output: Contribution to journalArticle

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