## Abstract A plane graph __G__ is coupled __k__βchoosable if, for any list assignment __L__ satisfying $|{{L}}({{x}})|= {{k}}$ for every ${{x}}\in {{V}}({{G}})\cup {{F}}({{G}})$, there is a coloring that assigns to each vertex and each face a color from its list such that any two adjacent or incid
On 3-choosability of triangle-free plane graphs
β Scribed by YingQian Wang; QiJun Zhang
- Publisher
- SP Science China Press
- Year
- 2011
- Tongue
- English
- Weight
- 234 KB
- Volume
- 54
- Category
- Article
- ISSN
- 1674-7283
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π SIMILAR VOLUMES
Thomassen, 1994 showed that all planar graphs are 5-choosable. In this paper we extend this result, by showing that all Ks-minor-free graphs are 5-choosable. (~) 1998 Elsevier Science B.V.
We show that for every k β₯ 1 and Ξ΄ > 0 there exists a constant c > 0 such that, with probability tending to 1 as n β β, a graph chosen uniformly at random among all triangle-free graphs with n vertices and M β₯ cn 3/2 edges can be made bipartite by deleting Ξ΄M edges. As an immediate consequence of th
A graph G=(V, E) is (x, y)-choosable for integers x> y 1 if for any given family In this paper, structures of some plane graphs, including plane graphs with minimum degree 4, are studied. Using these results, we may show that if G is free of k-cycles for some k # [3,4,5,6], or if any two triangles