### Abstract

Let C be a set of colors, and let ω(c) be an integer cost assigned to a color c in C. An edge-coloring of a graph G is to color all the edges of G so that any two adjacent edges are colored with different colors in C. The cost ω(f) of an edge-coloring f of G is the sum of costs ω(f(e)) of colors f(e) assigned to all edges e in G. An edge-coloring f of G is optimal if ω(f) is minimum among all edge-colorings of G. In this paper, we show that the problem of finding an optimal edge-coloring of a tree T can be simply reduced in polynomial time to the minimum weight perfect matching problem for a new bipartite graph constructed from T. The reduction immediately yields an efficient simple algorithm to find an optimal edge-coloring of T in time , where n is the number of vertices in T, Δ is the maximum degree of T, and N _{ω} is the maximum absolute cost |ω(c)| of colors c in C. We then show that our result can be extended for multitrees.

Original language | English |
---|---|

Title of host publication | Frontiers in Algorithmics - 4th International Workshop, FAW 2010, Proceedings |

Pages | 274-284 |

Number of pages | 11 |

DOIs | |

Publication status | Published - 2010 Aug 27 |

Event | 4th International Frontiers of Algorithmics Workshop, FAW 2010 - Wuhan, China Duration: 2010 Aug 11 → 2010 Aug 13 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 6213 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 4th International Frontiers of Algorithmics Workshop, FAW 2010 |
---|---|

Country | China |

City | Wuhan |

Period | 10/8/11 → 10/8/13 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'Minimum cost edge-colorings of trees can be reduced to matchings'. Together they form a unique fingerprint.

## Cite this

*Frontiers in Algorithmics - 4th International Workshop, FAW 2010, Proceedings*(pp. 274-284). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6213 LNCS). https://doi.org/10.1007/978-3-642-14553-7_26