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

Research output: Contribution to journalArticlepeer-review

Authors

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

Colleges, School and Institutes

External organisations

  • University of Colorado-Denver
  • Universität Rostock

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.

Details

Original languageEnglish
JournalElectronic Journal of Combinatorics
Volume19
Issue number2
Publication statusPublished - 28 Jun 2012