On the Chromatic Number of the Visibility Graph of a Set of Points in the Plane

被引：0

作者：

Jan Kára

Attila Pór

David R. Wood

机构：

[1] Department of Applied Mathematics,

[2] Charles University,undefined

[3] 118 00 Prague 1 ,undefined

[4] Department of Mathematics,undefined

[5] Case Western University,undefined

[6] Cleveland,undefined

[7] OH 44106,undefined

[8] Departament de Matematica Aplicada II,undefined

[9] Universitat Politecnica de Catalunya,undefined

[10] E-08034 Barcelona,undefined

来源：

Discrete & Computational Geometry | 2005年 / 34卷

关键词：

Computational Mathematic; Line Segment; Open Problem; Chromatic Number; Visibility Graph;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The visibility graph V(P) of a point set P \subseteq R2 has vertex set P, such that two points v,w ∈ P are adjacent whenever there is no other point in P on the line segment between v and w. We study the chromatic number of V(P). We characterise the 2- and 3-chromatic visibility graphs. It is an open problem whether the chromatic number of a visibility graph is bounded by its clique number. Our main result is a super-polynomial lower bound on the chromatic number (in terms of the clique number).

引用

页码：497 / 506

页数：9

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