We prove that every planar graph of girth at least 5 is 3-choosable. It is even possible to precolor any 5-cycle in the graph. This extension implies GrΓΆtzsch's theorem that every planar graph of girth at least 4 is 3-colorable. If 1995 Academic Press, Inc.
3-list-coloring planar graphs of girth 4
β Scribed by Jun-Lin Guo; Yue-Li Wang
- Book ID
- 108114287
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 263 KB
- Volume
- 311
- Category
- Article
- ISSN
- 0012-365X
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## Abstract Given an edge coloring __F__ of a graph __G__, a vertex coloring of __G__ is __adapted to F__ if no color appears at the same time on an edge and on its two endpoints. If for some integer __k__, a graph __G__ is such that given any list assignment __L__ to the vertices of __G__, with |_
The odd-girth of a graph is the length of a shortest odd circuit. A conjecture by Pavol Hell about circular coloring is solved in this article by showing that there is a function f ( ) for each : 0 < < 1 such that, if the odd-girth of a planar graph G is at least f ( ), then G is (2 + )-colorable. N