Perfect partition of some regular bipartite graphs

Chi-Kwong Li; Jeff Soosiah; Gexin Yu

Perfect partition of some regular bipartite graphs

Combinatorics 2012-12-27 v1

Authors: Chi-Kwong Li , Jeff Soosiah , Gexin Yu

Abstract

A graph has a perfect partition if all its perfect matchings can be partitioned so that each part is a 1-factorization of the graph. Let $L_{rm, r}=K_{rm,rm}-mK_{r,r}$ . We first give a formula to count the number of perfect matchings of $L_{rm, r}$ , then show that $L_{6,1}$ and $L_{8,2}$ have perfect partitions.

Keywords

perfect partition perfect matchings 1-factorization regular bipartite graphs graph theory

Cite

@article{arxiv.1212.6091,
  title  = {Perfect partition of some regular bipartite graphs},
  author = {Chi-Kwong Li and Jeff Soosiah and Gexin Yu},
  journal= {arXiv preprint arXiv:1212.6091},
  year   = {2012}
}

Comments

11 pages, 1 figure

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