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A general upper bound for the cyclic chromatic number of 3‐connected plane graphs
Author(s) -
Enomoto Hikoe,
Horňák Mirko
Publication year - 2009
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20383
Subject(s) - combinatorics , mathematics , chromatic scale , upper and lower bounds , graph , plane (geometry) , bound graph , graph power , planar graph , discrete mathematics , line graph , geometry , mathematical analysis
Abstract The cyclic chromatic number of a plane graph G is the smallest number χ c ( G ) of colors that can be assigned to vertices of G in such a way that whenever two distinct vertices are incident with a common face, they receive distinct colors. It was conjectured by Plummer and Toft in 1987 that, for every 3‐connected plane graph G , χ c ( G )≤Δ * ( G ) + 2, where Δ * ( G ) is the maximum face degree of G . The best upper bound known so far was Δ * ( G ) + 8. In the paper this bound is improved to Δ * ( G ) + 5. © 2009 Wiley Periodicals, Inc. J Graph Theory 62: 1–25, 2009