Location of Repository

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

Topics:
QA Mathematics

Publisher: Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science

Year: 2004

OAI identifier:
oai:eprints.lse.ac.uk:13346

Provided by:
LSE Research Online

Download PDF:To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.