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

被引：0
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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;
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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).
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页码：497 / 506
页数：9
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