Some results on (a:b)-choosability
| Autor: | Shai Gutner, Michael Tarsi |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Discrete mathematics
Mathematics::Combinatorics Voltage graph Butterfly graph Theoretical Computer Science law.invention Combinatorics Windmill graph Computer Science::Discrete Mathematics Graph power law Line graph Discrete Mathematics and Combinatorics Cubic graph Regular graph Graph toughness Mathematics |
| Zdroj: | Discrete Mathematics. 309:2260-2270 |
| ISSN: | 0012-365X |
| DOI: | 10.1016/j.disc.2008.04.061 |
| Popis: | A solution to a problem of Erdos, Rubin and Taylor is obtained by showing that if a graph G is (a:b)-choosable, and c/d>a/b, then G is not necessarily (c:d)-choosable. Applying probabilistic methods, an upper bound for the kth choice number of a graph is given. We also prove that a directed graph with maximum outdegree d and no odd directed cycle is (k(d+1):k)-choosable for every k>=1. Other results presented in this article are related to the strong choice number of graphs (a generalization of the strong chromatic number). We conclude with complexity analysis of some decision problems related to graph choosability. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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