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A note on cyclic chromatic number

100%

Zlámalová J.

Discussiones Mathematicae Graph Theory

2010

tom 30

nr 1

115-122

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 $χ_c(G)$ of G is the smallest number of colours in a cyclic colouring of G. Plummer and Toft in 1987 conjectured that $χ_c(G) ≤ Δ* + 2$ 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.

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1 Discussiones Mathematicae Graph Theory

1 Zlámalová J.

1 2010

Wyniki wyszukiwania

A note on cyclic chromatic number