## Abstract

A rainbow subgraph of an edge-coloured graph is a subgraph whose edges have distinct colours. The colour degree of a vertex v is the number of different colours on edges incident with v. Wang and Li conjectured that for k ≥ 4, every edge-coloured graph with minimum colour degree k contains a rainbow matching of size at least k/2. A properly edge-coloured K4 has no such matching, which motivates the restriction k ≥ 4, but Li and Xu proved the conjecture for all other properly coloured complete graphs. LeSaulnier, Stocker, Wenger and West showed that a rainbow matching of size k/2 is guaranteed to exist, and they proved several sufficient conditions for a matching of size k/2. We prove the conjecture in full.

Original language | English (US) |
---|---|

Pages (from-to) | 255-263 |

Number of pages | 9 |

Journal | Combinatorics Probability and Computing |

Volume | 21 |

Issue number | 1-2 |

DOIs | |

State | Published - Jan 1 2012 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics