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arXiv · 1207.2178

A note on large rainbow matchings in edge-coloured graphs

Allan Lo·Ta Sheng Tan
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Abstract

A rainbow subgraph in an edge-coloured graph is a subgraph such that its edges have distinct colours. The minimum colour degree of a graph is the smallest number of distinct colours on the edges incident with a vertex over all vertices. Kostochka, Pfender, and Yancey showed that every edge-coloured graph on $n$ vertices with minimum colour degree at least $k$ contains a rainbow matching of size at least $k$, provided $n\geq (17/4)k^2$. In this paper, we show that $n\geq 4k-4$ is sufficient for $k \ge 4$.

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Allan Lo, Ta Sheng Tan. 2012-07-09. A note on large rainbow matchings in edge-coloured graphs. https://arxiv.org/abs/1207.2178

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