Maximum matchings in regular graphs

Dong Ye

Maximum matchings in regular graphs

Combinatorics 2016-11-22 v3

Authors: Dong Ye

Abstract

It was conjectured by Mkrtchyan, Petrosyan, and Vardanyan that every graph $G$ with $\Delta(G)-\delta(G) \le 1$ has a maximum matching $M$ such that any two $M$ -unsaturated vertices do not share a neighbor. In this note, we confirm the conjecture for all $k$ -regular simple graphs and also $k$ -regular multigraphs with $k\le 4$ .

Keywords

hadwiger conjecture graph theory hypergraph theory

Cite

@article{arxiv.1308.2269,
  title  = {Maximum matchings in regular graphs},
  author = {Dong Ye},
  journal= {arXiv preprint arXiv:1308.2269},
  year   = {2016}
}

Comments

Fixed some incomplete arguments in the previous version

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