Half-regular factorizations of the complete bipartite graph

Mark Aksen, Istvan Miklos, Kathleen Zhou

Research output: Contribution to journalArticle


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
Publication statusPublished - Oct 30 2017


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

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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