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. (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: Articles
• Additional Information: Postprint provided by the author
• Keywords: Complexity; Graph; Colouring; Achromatic; b-chromatic
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Manlove, Professor 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.