### Abstract

We consider the problem of coloring edges of a graph subject to the following constraint: for every vertex v, all the edges incident to v have to be colored with at most q colors. The goal is to find a coloring satisfying the above constraint and using the maximum number of colors. This problem has been studied in the past from the combinatorial and algorithmic point of view. The optimal coloring is known for some special classes of graphs. There is also an approximation algorithm for general graphs, which in the case q = 2 gives a 2-approximation. However, the complexity of finding the optimal coloring was not known. We prove that for any integer q ≥ 2 the problem is NP-Hard and APX-Hard. We also present a 5/3-approximation algorithm for q = 2 for graphs with a perfect matching.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 132-143 |

Number of pages | 12 |

Volume | 6507 LNCS |

Edition | PART 2 |

DOIs | |

Publication status | Published - 2010 |

Externally published | Yes |

Event | 21st Annual International Symposium on Algorithms and Computations, ISAAC 2010 - Jeju Island, Korea, Republic of Duration: Dec 15 2010 → Dec 17 2010 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Number | PART 2 |

Volume | 6507 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 21st Annual International Symposium on Algorithms and Computations, ISAAC 2010 |
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Country | Korea, Republic of |

City | Jeju Island |

Period | 12/15/10 → 12/17/10 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(PART 2 ed., Vol. 6507 LNCS, pp. 132-143). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6507 LNCS, No. PART 2). https://doi.org/10.1007/978-3-642-17514-5_12

**Approximation and hardness results for the maximum edge q-coloring problem.** / Adamaszek, Anna; Popa, Alexandru.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*PART 2 edn, vol. 6507 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 2, vol. 6507 LNCS, pp. 132-143, 21st Annual International Symposium on Algorithms and Computations, ISAAC 2010, Jeju Island, Korea, Republic of, 12/15/10. https://doi.org/10.1007/978-3-642-17514-5_12

}

TY - GEN

T1 - Approximation and hardness results for the maximum edge q-coloring problem

AU - Adamaszek, Anna

AU - Popa, Alexandru

PY - 2010

Y1 - 2010

N2 - We consider the problem of coloring edges of a graph subject to the following constraint: for every vertex v, all the edges incident to v have to be colored with at most q colors. The goal is to find a coloring satisfying the above constraint and using the maximum number of colors. This problem has been studied in the past from the combinatorial and algorithmic point of view. The optimal coloring is known for some special classes of graphs. There is also an approximation algorithm for general graphs, which in the case q = 2 gives a 2-approximation. However, the complexity of finding the optimal coloring was not known. We prove that for any integer q ≥ 2 the problem is NP-Hard and APX-Hard. We also present a 5/3-approximation algorithm for q = 2 for graphs with a perfect matching.

AB - We consider the problem of coloring edges of a graph subject to the following constraint: for every vertex v, all the edges incident to v have to be colored with at most q colors. The goal is to find a coloring satisfying the above constraint and using the maximum number of colors. This problem has been studied in the past from the combinatorial and algorithmic point of view. The optimal coloring is known for some special classes of graphs. There is also an approximation algorithm for general graphs, which in the case q = 2 gives a 2-approximation. However, the complexity of finding the optimal coloring was not known. We prove that for any integer q ≥ 2 the problem is NP-Hard and APX-Hard. We also present a 5/3-approximation algorithm for q = 2 for graphs with a perfect matching.

UR - http://www.scopus.com/inward/record.url?scp=78650963895&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650963895&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-17514-5_12

DO - 10.1007/978-3-642-17514-5_12

M3 - Conference contribution

SN - 3642175163

SN - 9783642175169

VL - 6507 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 132

EP - 143

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

ER -