## Abstract A proper vertex coloring of a graph __G__β=β(__V,E__) is acyclic if __G__ contains no bicolored cycle. A graph __G__ is acyclically __L__βlist colorable if for a given list assignment __L__β=β{__L__(__v__): __v__:βββ__V__}, there exists a proper acyclic coloringβΟβof __G__ such that Ο(_
Acyclic Edge Coloring of Planar Graphs Without Small Cycles
β Scribed by Jianfeng Hou; Guizhen Liu; Jianliang Wu
- Publisher
- Springer Japan
- Year
- 2011
- Tongue
- English
- Weight
- 205 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
An __acyclic__ edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The __acyclic chromatic index__ of a graph is the minimum number __k__ such that there is an acyclic edge coloring using __k__ colors and is denoted by __a__β²(__G__). It was conjectured by Al
## Abstract It is well known that every planar graph __G__ is 2βcolorable in such a way that no 3βcycle of __G__ is monochromatic. In this paper, we prove that __G__ has a 2βcoloring such that no cycle of length 3 or 4 is monochromatic. The complete graph __K__~5~ does not admit such a coloring. On
The conjecture on acyclic 5-choosability of planar graphs [Borodin et al., 2002] as yet has been verified only for several restricted classes of graphs. None of these classes allows 4-cycles. We prove that a planar graph is acyclically 5-choosable if it does not contain an i-cycle adjacent to a j-cy
## Abstract The acyclic list chromatic number of every planar graph is proved to be at most 7. Β© 2002 Wiley Periodicals, Inc. J Graph Theory 40: 83β90, 2002