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.
Original language | English |
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Journal | Electronic Journal of Combinatorics |
Volume | 19 |
Issue number | 2 |
Publication status | Published - 28 Jun 2012 |
Keywords
- Properly edge-colored graphs
- Rainbow matching
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics