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The list chromatic numbers of some planar graphs

✍ Scribed by Lü Enyue; Zhang Kemin

Publisher
SP Editorial Committee of Applied Mathematics - A Journal of Chinese Universities
Year
1999
Tongue
English
Weight
438 KB
Volume
14
Category
Article
ISSN
1005-1031

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The concept of the star chromatic number of a graph was introduced by Vince (A. Vince, Star chromatic number, J. Graph Theory 12 (1988), 551--559), which is a natural generalization of the chromatic number of a graph. This paper calculates the star chromatic numbers of three infinite families of pla

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## Abstract In 1959, even before the Four‐Color Theorem was proved, Grötzsch showed that planar graphs with girth at least 4 have chromatic number at the most 3. We examine the fractional analogue of this theorem and its generalizations. For any fixed girth, we ask for the largest possible fraction

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## Abstract The vertex set of the reduced Kneser graph KG~2~(__m,2__) consists of all pairs {__a,b__} such that __a, b__ε{1,2,…,__m__} and 2≤|__a__−__b__|≤__m__−2. Two vertices are defined to be adjacent if they are disjoint. We prove that, if __m__≥4 __and m__≠5, then the circular chromatic number