### Abstract

In an edge-coloring of a graph G = (V, E) each color appears around each vertex at most once. An f-coloring is a generalization of an edge-coloring in which each color appears around each vertex v at most f(υ) times where f is a function assigning a natural number f(υ) ∊ N to each vertex υ ∊ V. In this paper we first give a simple reduction of the f-coloring problem to the ordinary edge-coloring problem, that is, we show that, given a graph G = (V, E) and a function f: υ → N, one can directly construct in polynomial-time a new simple graph whose edge-coloring using a minimum number of colors immediately induces an f-coloring of G using a minimum number of colors. As by-products, we give a necessary and sufficient condition for a graph to have an f-factorization, and show that the edge-coloring problem for multigraphs can be easily reduced to edge-coloring problems for simple graphs.

Original language | English |
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Title of host publication | Computing and Combinatorics - 1st Annual International Conference, COCOON 1995, Proceedings |

Editors | Ding-Zhu Du, Ming Li, Ding-Zhu Du |

Publisher | Springer-Verlag |

Pages | 223-228 |

Number of pages | 6 |

ISBN (Print) | 354060216X, 9783540602163 |

DOIs | |

Publication status | Published - 1995 Jan 1 |

Event | 1st Annual International Computing and Combinatorics Conference, COCOON 1995 - Xi’an, China Duration: 1995 Aug 24 → 1995 Aug 26 |

### 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 | 959 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 1st Annual International Computing and Combinatorics Conference, COCOON 1995 |
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Country | China |

City | Xi’an |

Period | 95/8/24 → 95/8/26 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Computing and Combinatorics - 1st Annual International Conference, COCOON 1995, Proceedings*(pp. 223-228). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 959). Springer-Verlag. https://doi.org/10.1007/BFb0030836