Rainbow Matchings of size \delta(G) in Properly Edge-colored Graphs
Combinatorics
2011-08-15 v1
Abstract
A {\it rainbow matching} in an edge-colored graph is a matching in which all the edges have distinct colors. Wang asked if there is a function f(\delta) such that a properly edge-colored graph G with minimum degree \delta and order at least f(\delta) must have a rainbow matching of size \delta. We answer this question in the affirmative; f(\delta) = 6.5\delta suffices. Furthermore, the proof provides a O(\delta(G)|V(G)|^2)-time algorithm that generates such a matching.
Cite
@article{arxiv.1108.2521,
title = {Rainbow Matchings of size \delta(G) in Properly Edge-colored Graphs},
author = {Jennifer Diemunsch and Michael Ferrara and Casey Moffatt and Florian Pfender and Paul S. Wenger},
journal= {arXiv preprint arXiv:1108.2521},
year = {2011}
}