Borodin, O. V., Broersma, H. J., Glebov, A. and van den Heuvel, Jan 
ORCID: 0000-0003-0897-9148
(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.
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 |
| Divisions: | Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 20 Nov 2008 10:34 |
| Last Modified: | 13 Sep 2024 16:31 |
| URI: | http://eprints.lse.ac.uk/id/eprint/13346 |
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