Large Rainbow Matchings in Edge-Colored Graphs
نویسندگان
چکیده
A rainbow subgraph of an edge-colored graph is a subgraph whose edges have distinct colors. The color degree of a vertex v is the number of different colors on edges incident with v. Wang and Li conjectured that for k ≥ 4, every edge-colored graph with minimum color degree k contains a rainbow matching of size at least dk/2e. A properly edge-colored K4 has no such matching, which motivates the restriction k ≥ 4, but Li and Xu proved the conjecture for all other properly colored complete graphs. LeSaulnier, Stocker, Wenger, and West showed that a rainbow matching of size bk/2c is guaranteed to exist, and they proved several sufficient conditions for a matching of size dk/2e. We prove the conjecture in full. 2000 Mathematics Subject Classification: 05C15, 05C35.
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