Rainbow matchings of size δ(G) in properly edge-colored graphs

Abstract

A 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(δ) such that a properly edge-colored graph G with minimum degree δ and order at least f(δ) must have a rainbow matching of size δ. We answer this question in the affirmative; an extremal approach yields that f(δ) = 98δ/23 < 4.27δ suffices. Furthermore, we give an O(δ(G)\V(G)\ 2)-time algorithm that generates such a matching in a properly edge-colored graph of order at least 6.5δ.