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Three new upper bounds on the chromatic number

✍ Scribed by María Soto; André Rossi; Marc Sevaux


Book ID
113564665
Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
238 KB
Volume
159
Category
Article
ISSN
0166-218X

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## Abstract A cyclic coloring of a plane graph is a vertex coloring such that vertices incident with the same face have distinct colors. The minimum number of colors in a cyclic coloring of a graph is its cyclic chromatic number χ^__c__^. Let Δ^\*^ be the maximum face degree of a graph. There exist

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The entire chromatic number χ ve f (G) of a plane graph G is the least number of colors assigned to the vertices, edges and faces so that every two adjacent or incident pair of them receive different colors. conjectured that χ ve f (G) ≤ + 4 for every plane graph G. In this paper we prove the conj