A Characterization of Graphs with Fractional Total Chromatic Number Equal to Δ + 2

Takehiro Ito, W. Sean Kennedy, Bruce A. Reed

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

For a simple graph of maximum degree Δ, the complexity of computing the fractional total chromatic number is unknown. Trivially it is at least Δ + 1. Kilakos and Reed proved that it is at most Δ + 2. In this paper, we strengthen this by characterizing exactly those simple graphs with fractional total chromatic number Δ + 2. This yields a simple linear-time algorithm to determine whether a given graph has fractional chromatic number Δ + 2. Crown

Original languageEnglish
Pages (from-to)235-240
Number of pages6
JournalElectronic Notes in Discrete Mathematics
Volume35
Issue numberC
DOIs
Publication statusPublished - 2009 Dec 1

Keywords

  • edge colouring
  • fractional total colouring
  • graph theory

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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