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A new upper bound on the cyclic chromatic number

Borodin, O. V., Broersma, H. J., Glebov, A. and van den Heuvel, Jan (2004) A new upper bound on the cyclic chromatic number. CDAM research report series, LSE-CDAM-2004-04. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

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Abstract

A cyclic colouring of a plane graph is a vertex colouring such that vertices incident with the same face have distinct colours. The minimum number of colours in a cyclic colouring of a graph is its cyclic chromatic number Âc. Let ¢¤ be the maximum face degree of a graph. There exist plane graphs with Âc = b3 2 ¢¤c. Ore and Plummer (1969) proved that Âc · 2¢¤, which bound was improved to b9 5 ¢¤c by Borodin, Sanders and Zhao (1999), and to d5 3 ¢¤e by Sanders and Zhao (2001). We introduce a new parameter k¤, which is the maximum number of vertices that two faces of a graph can have in common, and prove that Âc · max{¢¤ + 3 k¤ + 2, ¢¤ + 14, 3 k¤ + 6, 18 }, and if ¢¤ ¸ 4 and k¤ ¸ 4, then Âc · ¢¤ + 3 k¤ + 2.

Item Type: Monograph (Report)
Official URL: http://www.cdam.lse.ac.uk
Additional Information: © 2004 the authors
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: LSE-CDAM-2004-04
Date Deposited: 20 Nov 2008 10:34
URL: http://eprints.lse.ac.uk/13346/

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