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The b-chromatic number of a graph

Irving, R.W., and Manlove, D.F. (1999) The b-chromatic number of a graph. Discrete Applied Mathematics, 91 (1-3). pp. 127-141. ISSN 0166-218X (doi:10.1016/S0166-218X(98)00146-2)

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Publisher's URL: http://dx.doi.org/doi:10.1016/S0166-218X(98)00146-2

Abstract

The achromatic number psi(G) of a graph G = (V,E) is the maximum k such that V has a partition V1, V2,...,Vk into independent sets, the union of no pair of which is independent. Here we show that psi(G) can be viewed as the maximum over all minimal elements of a partial order defined on the set of all colourings of G. We introduce a natural refinement of this partial order, giving rise to a new parameter, which we call the b-chromatic number, varphi(G), of G. We prove that determining varphi(G) is NP-hard for general graphs, but polynomial-time solvable for trees.

Item Type:Article
Additional Information:Postprint provided by the author
Keywords:Complexity; Graph; Colouring; Achromatic; b-chromatic
Status:Published
Refereed:Yes
Glasgow Author(s):Manlove, Dr David
Authors: Irving, R.W., and Manlove, D.F.
Subjects:Q Science > QA Mathematics > QA75 Electronic computers. Computer science
College/School:College of Science and Engineering > School of Computing Science
Research Group:Formal Analysis, Theory and Algorithms
Journal Name:Discrete Applied Mathematics
Publisher:Elsevier
ISSN:0166-218X
Copyright Holders:©1999 Published by Elsevier Science B.V.
First Published:First published in Discrete Applied Mathematics 91(1-3):127-141
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher.

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