Rainbow Matching in Edge-Colored Graphs

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 to v. Wang and Li conjectured that for k > 4, every edge-colored graph with minimum color degree at least k contains a rainbow matching of size at least ⌈k/2⌉. We prove the slightly weaker statement that a rainbow matching of size at least ⌊k/2⌋ is guaranteed. We also give sufficient conditions for a rainbow matching of size at least ⌈k/2⌉ that fail to hold only for finitely many exceptions (for each odd k).