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On the Entire Coloring Conjecture

Published online by Cambridge University Press:  20 November 2018

Daniel P. Sanders  and
Yue Zhao
Daniel P. Sanders
Affiliation:
23 Cliff Road Belle Terre, NY 11777 USA, email: dan@rentec.com
Yue Zhao
Affiliation:
Department of Mathematics University of Central Florida PO Box 161364 Orlando, FL 32816-1364 USA, email: yzhao@pegasus.cc.ucf.edu
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Abstract

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The Four Color Theorem says that the faces (or vertices) of a plane graph may be colored with four colors. Vizing’s Theorem says that the edges of a graph with maximum degree $\Delta$ may be colored with $\Delta \,+\,1$ colors. In 1972, Kronk and Mitchem conjectured that the vertices, edges, and faces of a plane graph may be simultaneously colored with $\Delta \,+\,4$ colors. In this article, we give a simple proof that the conjecture is true if $\Delta \,\ge \,6$.

Keywords

05C1505C10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 43 , Issue 1 , 01 March 2000 , pp. 108 - 114
Copyright
Copyright © Canadian Mathematical Society 2000

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