Simple reduction of f-colorings to edge-colorings

Xiao Zhou, Takao Nishizeki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

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 languageEnglish
Title of host publicationComputing and Combinatorics - 1st Annual International Conference, COCOON 1995, Proceedings
EditorsDing-Zhu Du, Ming Li, Ding-Zhu Du
PublisherSpringer-Verlag
Pages223-228
Number of pages6
ISBN (Print)354060216X, 9783540602163
DOIs
Publication statusPublished - 1995 Jan 1
Event1st Annual International Computing and Combinatorics Conference, COCOON 1995 - Xi’an, China
Duration: 1995 Aug 241995 Aug 26

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume959
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other1st Annual International Computing and Combinatorics Conference, COCOON 1995
CountryChina
CityXi’an
Period95/8/2495/8/26

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Zhou, X., & Nishizeki, T. (1995). Simple reduction of f-colorings to edge-colorings. In D-Z. Du, M. Li, & D-Z. Du (Eds.), 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