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Precoloring Extension III: Classes of Perfect Graphs

Published online by Cambridge University Press:  12 September 2008

M. Hujter  and
Zs. Tuza
M. Hujter
Affiliation:
Mathematics Institute, University of Miskolc, Miskolc-Egyetemváros 3515, Hungary
Zs. Tuza
Affiliation:
Computer and Automation Institute, Hungarian Academy of Sciences, Kende u. 13–17, Budapest 1111, Hungary
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Abstract

We continue the study of the following general problem on the vertex colourings of graphs. Suppose that some vertices of a graph G are assigned to some colours. Can this ‘precolouring’ be extended to a proper colouring of G with at most k colours (for some given k)? Here we investigate the complexity status of precolouring extendibility on some classes of perfect graphs, giving good characterizations (necessary and sufficient conditions) that lead to algorithms with linear or polynomial running time. It is also shown how a larger subclass of perfect graphs can be derived from graphs containing no induced path on four vertices.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 1 , March 1996 , pp. 35 - 56
Copyright
Copyright © Cambridge University Press 1996

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