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arXiv · 1602.04316

Half-regular factorizations of the complete bipartite graph

Mark Aksen·Istvan Miklos·Kathleen Zhou
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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 are polynomial bounded. Realizations of a half-regular degree matrix are generalizations of Latin squares, and they also appear in applied neuroscience.

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Mark Aksen, Istvan Miklos, Kathleen Zhou. 2016-02-13. Half-regular factorizations of the complete bipartite graph. https://arxiv.org/abs/1602.04316

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