## It is proved that a planar graph G without five cycles is three degenerate, hence, four choosable, and it is also edge-(A( G) + l)-h
Structural properties and edge choosability of planar graphs without 4-cycles
β Scribed by Yufa Shen; Guoping Zheng; Wenjie He; Yongqiang Zhao
- Book ID
- 108113926
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 288 KB
- Volume
- 308
- Category
- Article
- ISSN
- 0012-365X
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## Abstract A proper vertex coloring of a graph __G__=(__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__={__L__(__v__)|__v__β__V__}, there exists a proper acyclic coloring Ο of __G__ such that Ο(__v__)β_
## 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(_
A graph G is called k-choosable if k is a number such that if we give lists of k colors to each vertex of G there is a vertex coloring of G where each vertex receives a color from its own list no matter what the lists are. In this paper, it is shown that each plane graph without 4-cycles is 4-choosa