### 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: Min-max edge q-coloring is NP-hard, for any q ≥ 2. A polynomial time exact algorithm for min-max edge q-coloring on trees. Exact formulas of the optimal solution for cliques and almost tight bounds for bicliques and hypergraphs. A non-trivial lower bound of the optimal solution with respect to the average degree of the graph. An approximation algorithm for planar graphs.

Original language | English |
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Pages (from-to) | 505-528 |

Number of pages | 24 |

Journal | Journal of Graph Algorithms and Applications |

Volume | 19 |

Issue number | 1 |

DOIs | |

Publication status | Published - Aug 1 2015 |

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### ASJC Scopus subject areas

- Computer Science(all)
- Computer Science Applications
- Geometry and Topology
- Theoretical Computer Science
- Computational Theory and Mathematics

### Cite this

*Journal of Graph Algorithms and Applications*,

*19*(1), 505-528. https://doi.org/10.7155/jgaa.00373

**The min-max edge q-coloring problem.** / Larjomaa, Tommi; Popa, Alexandru.

Research output: Contribution to journal › Article

*Journal of Graph Algorithms and Applications*, vol. 19, no. 1, pp. 505-528. https://doi.org/10.7155/jgaa.00373

}

TY - JOUR

T1 - The min-max edge q-coloring problem

AU - Larjomaa, Tommi

AU - Popa, Alexandru

PY - 2015/8/1

Y1 - 2015/8/1

N2 - 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: Min-max edge q-coloring is NP-hard, for any q ≥ 2. A polynomial time exact algorithm for min-max edge q-coloring on trees. Exact formulas of the optimal solution for cliques and almost tight bounds for bicliques and hypergraphs. A non-trivial lower bound of the optimal solution with respect to the average degree of the graph. An approximation algorithm for planar graphs.

AB - 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: Min-max edge q-coloring is NP-hard, for any q ≥ 2. A polynomial time exact algorithm for min-max edge q-coloring on trees. Exact formulas of the optimal solution for cliques and almost tight bounds for bicliques and hypergraphs. A non-trivial lower bound of the optimal solution with respect to the average degree of the graph. An approximation algorithm for planar graphs.

UR - http://www.scopus.com/inward/record.url?scp=84951292325&partnerID=8YFLogxK

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U2 - 10.7155/jgaa.00373

DO - 10.7155/jgaa.00373

M3 - Article

AN - SCOPUS:84951292325

VL - 19

SP - 505

EP - 528

JO - Journal of Graph Algorithms and Applications

JF - Journal of Graph Algorithms and Applications

SN - 1526-1719

IS - 1

ER -