# A new upper bound on the cyclic chromatic number

Borodin, O.V.
and
Broersma, H.J.
and
Glebov, A.
and
Heuvel, J. van den
(2006)
*A new upper bound on the cyclic chromatic number.*
Journal of Graph Theory, 54
(1).
pp. 58-72.
ISSN 0364-9024

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Abstract: | A cyclic coloring of a plane graph is a vertex coloring such that vertices incident with the same face have distinct colors. The minimum number of colors in a cyclic coloring of a graph is its cyclic chromatic number . Let be the maximum face degree of a graph. There exist plane graphs with . Ore and Plummer [5] proved that , which bound was improved to by Borodin, Sanders, and Zhao [1], and to by Sanders and Zhao [7].
We introduce a new parameter , which is the maximum number of vertices that two faces of a graph can have in common, and prove that , and if and , then . |

Item Type: | Article |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/63866 |

Official URL: | http://dx.doi.org/10.1002/jgt.20193 |

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Metis ID: 237816