Rainbow Matchings of size δ(G) in Properly Edge-colored Graphs

Jennifer Diemunsch, Michael Ferrara, Casey Moffatt, Florian Pfender, Paul S. Wenger

Published 2011-08-11Version 1

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.