Sufficient conditions for the existence of perfect heterochromatic matchings in colored graphs

Authors:
Lin Hu;Xueliang Li
Affiliations:
Center for Combinatorics and LPMC Nankai University, Tianjin, China;Center for Combinatorics and LPMC Nankai University, Tianjin, China
Venue:
CJCDGCGT'05 Proceedings of the 7th China-Japan conference on Discrete geometry, combinatorics and graph theory
Year:
2005

Citing 3
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Abstract

Let G = (V, E) be an edge-colored graph. A matching of G is called heterochromatic if its any two edges have different colors. Unlike uncolored matchings for which the maximum matching problem is solvable in polynomial time, the maximum heterochromatic matching problem is NP-complete. This means that to find both sufficient and necessary good conditions for the existence of perfect heterochromatic matchings should be not easy. In this paper, we obtain sufficient conditions of Hall-type and Tutte-type for the existence of perfect heterochromatic matchings in colored bipartite graphs and general colored graphs. We also obtain a sufficient and necessary condition of Berge-type to verify if a heterochromatic matching M of G is maximum.