On the number of $r$-matchings in a Tree
Combinatorics
2014-11-18 v2
Abstract
An -matching in a graph is a collection of edges in such that the distance between any two edges is at least . A -matching is also called an induced matching. In this paper, we estimate the maximum number of -matchings in a tree of fixed order. We also prove that the -vertex path has the maximum number of induced matchings among all -vertex trees.
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}
}