Total colorings of degenerated graphs

Shuji Isobe, Xiao Zhou, Takao Nishizeki

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

9 Citations (Scopus)

Abstract

A total coloring of a graph G is a coloring of all elements of G, i.e. vertices and edges, in such a way that no two adjacent or incident elements receive the same color. A graph G is s-degenerated for a positive integer s if G can be reduced to a trivial graph by successive removal of vertices with degree ≤ s. We prove that an s-degenerated graph G has a total coloring with δ + 1 colors if the maximum degree δ of G is su-ciently large, say δ ≥ 4s+3. Our proof yields an eficient algorithm to find such a total coloring. We also give a linear-time algorithm to find a total coloring of a graph G with the minimum number of colors if G is a partial k-tree, i.e. the tree-width of G is bounded by a fixed integer k.

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings
EditorsFernando Orejas, Paul G. Spirakis, Jan van Leeuwen
PublisherSpringer Verlag
Pages506-517
Number of pages12
ISBN (Print)3540422870, 9783540422877
DOIs
Publication statusPublished - 2001 Jan 1
Event28th International Colloquium on Automata, Languages and Programming, ICALP 2001 - Crete, Greece
Duration: 2001 Jul 82001 Jul 12

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2076 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other28th International Colloquium on Automata, Languages and Programming, ICALP 2001
CountryGreece
CityCrete
Period01/7/801/7/12

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Isobe, S., Zhou, X., & Nishizeki, T. (2001). Total colorings of degenerated graphs. In F. Orejas, P. G. Spirakis, & J. van Leeuwen (Eds.), Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings (pp. 506-517). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2076 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-48224-5_42