## Abstract

In this paper we introduce and study a new problem named min-max edge q-coloring which is motivated by applications in wireless mesh networks. The input of the problem consists of an undirected graph and an integer q. The goal is to color the edges of the graph with as many colors as possible such that: (a) any vertex is incident to at most q different colors, and (b) the maximum size of a color group (i.e. set of edges identically colored) is minimized. We show the following results: 1. Min-max edge q-coloring is NP-hard, for any q ≥ 2. 2. A polynomial time exact algorithm for min-max edge q-coloring on trees. 3. Exact formulas of the optimal solution for cliques. 4. An approximation algorithm for planar graphs.

Original language | English |
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Title of host publication | Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers |

Publisher | Springer Verlag |

Pages | 226-237 |

Number of pages | 12 |

Volume | 8986 |

ISBN (Electronic) | 9783319193144 |

DOIs | |

Publication status | Published - 2014 |

MoE publication type | A4 Article in a conference publication |

Event | International Workshop on Combinatorial Algorithms - Duluth, United States Duration: 15 Oct 2014 → 17 Oct 2014 Conference number: 25 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8986 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | International Workshop on Combinatorial Algorithms |
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Abbreviated title | IWOCA |

Country | United States |

City | Duluth |

Period | 15/10/2014 → 17/10/2014 |