Total Colorings of Planar Graphs without Small Cycles
β Scribed by Jianfeng Hou; Yan Zhu; Guizhen Liu; Jianliang Wu; Mei Lan
- Publisher
- Springer Japan
- Year
- 2008
- Tongue
- English
- Weight
- 197 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
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## 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
## 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(_