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Upper Bounds of Entire Chromatic Number of Plane Graphs

Authors
Journal
European Journal of Combinatorics
0195-6698
Publisher
Elsevier
Publication Date
Volume
20
Issue
4
Identifiers
DOI: 10.1006/eujc.1998.0258

Abstract

Abstract The1999 Academic Pressentire chromatic number χ Copyright vef ( G) of a plane graph Gis 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. Kronk and Mitchem (1973) conjectured that χ vef ( G) ≤ Δ + 4 for every plane graph G. In this paper we prove the conjecture for a plane graph Ghaving χ′( G) = Δ and give a upper bound χ vef ( G) ≤ Δ+5 for all plane graphs, where χ′( G) and Δ are the chromatic index and the maximum degree of G, respectively.

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