### 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 |
---|---|

Pages (from-to) | 21-33 |

Number of pages | 13 |

Journal | Discrete Applied Mathematics |

Volume | 230 |

DOIs | |

Publication status | Published - Oct 30 2017 |

### Fingerprint

### 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

*Discrete Applied Mathematics*,

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

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

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 230, pp. 21-33. https://doi.org/10.1016/j.dam.2017.06.003

}

TY - JOUR

T1 - Half-regular factorizations of the complete bipartite graph

AU - Aksen, Mark

AU - Miklós, I.

AU - Zhou, Kathleen

PY - 2017/10/30

Y1 - 2017/10/30

N2 - 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.

AB - 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.

KW - Degree matrix

KW - Degree sequences

KW - Edge packing

KW - Graph factorization

KW - Latin squares

KW - Markov chain Monte Carlo

UR - http://www.scopus.com/inward/record.url?scp=85026230759&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85026230759&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2017.06.003

DO - 10.1016/j.dam.2017.06.003

M3 - Article

AN - SCOPUS:85026230759

VL - 230

SP - 21

EP - 33

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -