A new upper bound for the list chromatic number
نویسندگان
چکیده
منابع مشابه
A new upper bound on the cyclic chromatic number
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 χc . Let ∗ be themaximum face degree of a graph. There exist plane graphs with χc = 2 ∗ . Ore and Plummer [5] proved that χc ≤ 2 ∗, which bound was improved to 5 ∗ by Borodin, Sand...
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Suppose that G is a graph with maximum degree d(G) and for every vertex v in G, the neighborhood of v contains at most d(G)2/f (f > 1) edges. We show that the list chromatic number of G is at most Kd(G)/ log f , for some positive constant K. This result is sharp up to the multiplicative constant K and strengthens previous results by Kim [Kim], Johansson [Joh], Alon, Krivelevich and Sudakov [AKS...
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Suppose that G is a graph with maximum degree ∆ and for every vertex v in G, the neighborhood of v contains at most ∆2/f edges. We prove that the list chromatic number of G is at most K∆/ log f , for some positive constant K. This result strengthens several previous results [AKSu2, Kim, Joh, Vu1] and is sharp up to the multiplicative constant K. As an application, we shall derive several upper ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1989
ISSN: 0012-365X
DOI: 10.1016/0012-365x(89)90199-4