A note on cyclic chromatic number
Jana Zlámalová
Discussiones Mathematicae Graph Theory, Tome 30 (2010), p. 115-122 / Harvested from The Polish Digital Mathematics Library
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A cyclic colouring of a graph G embedded in a surface is a vertex colouring of G in which any two distinct vertices sharing a face receive distinct colours. The cyclic chromatic number χc(G) of G is the smallest number of colours in a cyclic colouring of G. Plummer and Toft in 1987 conjectured that χc(G)≤Δ*+2 for any 3-connected plane graph G with maximum face degree Δ*. It is known that the conjecture holds true for Δ* ≤ 4 and Δ* ≥ 18. The validity of the conjecture is proved in the paper for some special classes of planar graphs.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:270892 
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Jana Zlámalová. A note on cyclic chromatic number. Discussiones Mathematicae Graph Theory, Tome 30 (2010) pp. 115-122. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1481/

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