Recolouring-resistant colourings

Authors:
Anders Sune Pedersen;Dieter Rautenbach
Affiliations:
Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark;Institut für Optimierung und Operations Research, Universität Ulm, D-89069 Ulm, Germany
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

We study colourings of graphs with the property that the number of used colours cannot be reduced by applying some recolouring operation. A well-studied example of such colourings are b-colourings, which were introduced by Irving and Manlove [R.W. Irving, D.F. Manlove, The b-chromatic number of a graph, Discrete Appl. Math. 91 (1999) 127-141]. Given a graph and a colouring, a recolouring operation specifies a set of vertices of the graph on which the colouring can be changed. We consider two such operations: One which allows the recolouring of all vertices within some given distance of some colour class, and another which allows the recolouring of all vertices that belong to one of a given number of colour classes. Our results extend known results concerning b-colourings and the associated b-chromatic number.