### 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 language | English |
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Pages (from-to) | 21-33 |

Number of pages | 13 |

Journal | Discrete Applied Mathematics |

Volume | 230 |

DOIs | |

Publication status | Published - Oct 30 2017 |

### 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

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## Cite this

*Discrete Applied Mathematics*,

*230*, 21-33. https://doi.org/10.1016/j.dam.2017.06.003