The 4-Choosability of Plane Graphs without 4-Cycles

Peter Che Bor Lam; Baogang Xu; Jiazhuang Liu

doi:10.1006/jctb.1998.1893

The 4-Choosability of Plane Graphs without 4-Cycles

Peter Che Bor Lam^*, Baogang Xu, Jiazhuang Liu

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › peer-review

63 Citations (Scopus)

Abstract

A graphGis calledk-choosable ifkis a number such that if we give lists ofkcolors to each vertex ofGthere is a vertex coloring ofGwhere 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-choosable.

Original language	English
Pages (from-to)	117-126
Number of pages	10
Journal	Journal of Combinatorial Theory. Series B
Volume	76
Issue number	1
DOIs	https://doi.org/10.1006/jctb.1998.1893
Publication status	Published - May 1999
Externally published	Yes

User-Defined Keywords

4-cycle
Choosability
List coloring
Plane graph

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10.1006/jctb.1998.1893

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abstract = "A graphGis calledk-choosable ifkis a number such that if we give lists ofkcolors to each vertex ofGthere is a vertex coloring ofGwhere 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-choosable.",

keywords = "4-cycle, Choosability, List coloring, Plane graph",

author = "{Che Bor Lam}, Peter and Baogang Xu and Jiazhuang Liu",

note = "Funding Information: Research is partially supported by Research Grant Council, Hong Kong; by Faculty Research Grant, Hong Kong Baptist University and by the Doctoral Foundation of the Education Commission of the The People{\textquoteright}s Republic of China.",

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N2 - A graphGis calledk-choosable ifkis a number such that if we give lists ofkcolors to each vertex ofGthere is a vertex coloring ofGwhere 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-choosable.

AB - A graphGis calledk-choosable ifkis a number such that if we give lists ofkcolors to each vertex ofGthere is a vertex coloring ofGwhere 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-choosable.

KW - 4-cycle

KW - Choosability

KW - List coloring

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The 4-Choosability of Plane Graphs without 4-Cycles

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