A note on cyclic chromatic number
نویسنده
چکیده
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) ≤ ∆∗ + 2 for any 3-connected plane graph G with maximum face degree ∆∗. It is known that the conjecture holds true for ∆∗ ≤ 4 and ∆∗ ≥ 18. The validity of the conjecture is proved in the paper for some special classes of planar graphs.
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عنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 30 شماره
صفحات -
تاریخ انتشار 2010