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Discrete Mathematics
Volume 111, Issues 1-3, 22 February 1993, Pages 389-392
 
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doi:10.1016/0012-365X(93)90175-S    How to Cite or Link Using DOI (Opens New Window)
Copyright © 1993 Published by Elsevier Science B.V. All rights reserved.

An upper bound for total colouring of graphs

Colin J. H. McDiarmid

Abdón Sánchez-Arroyo*

Department of Statistics, University of Oxford, Oxford, UK Linacre College and Mathematical Institute, University of Oxford, Oxford, UK

Received 22 July 1991. 
Available online 2 April 2002.

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Abstract

We give an upper bound on the number of colours required to extend a given vertex colouring of a graph to a total colouring. This shows that for any simple graph there is a total colouring using at most Image Δ + 3 colours, where Δ is the maximum vertex degree.

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Discrete Mathematics
Volume 111, Issues 1-3, 22 February 1993, Pages 389-392
 
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