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; f(δ) = 6.5δ suffices. Furthermore, the proof provides a O(δ(G)|V(G)|2)-time algorithm that generates such a matching.
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