English

On the number of $r$-matchings in a Tree

Combinatorics 2014-11-18 v2

Abstract

An rr-matching in a graph GG is a collection of edges in GG such that the distance between any two edges is at least rr. A 22-matching is also called an induced matching. In this paper, we estimate the maximum number of rr-matchings in a tree of fixed order. We also prove that the nn-vertex path has the maximum number of induced matchings among all nn-vertex trees.

Keywords

Cite

@article{arxiv.1409.7795,
  title  = {On the number of $r$-matchings in a Tree},
  author = {Dong Yeap Kang and Jaehoon Kim and Younjin Kim and Hiu-Fai Law},
  journal= {arXiv preprint arXiv:1409.7795},
  year   = {2014}
}