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

共 50 条

[21] THE STAR CHROMATIC NUMBER OF A GRAPH
ABBOTT, HL
ZHOU, B
JOURNAL OF GRAPH THEORY, 1993, 17 (03) : 349 - 360
[22] An approximate chromatic number of a graph
Marcu, Danut
JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY, 2008, 11 (04): : 461 - 464
[23] The chromatic number of a signed graph
Macajova, Edita
Raspaud, Andre
Skoviera, Martin
ELECTRONIC JOURNAL OF COMBINATORICS, 2016, 23 (01):
[24] On the quantum chromatic number of a graph
Cameron, Peter J.
Montanaro, Ashley
Newman, Michael W.
Severini, Simone
Winter, Andreas
ELECTRONIC JOURNAL OF COMBINATORICS, 2007, 14 (01):
[25] The chromatic covering number of a graph
Naserasr, R
Tardif, C
JOURNAL OF GRAPH THEORY, 2006, 51 (03) : 199 - 204
[26] The chromatic number of graph powers
Alon, N
Mohar, B
COMBINATORICS PROBABILITY & COMPUTING, 2002, 11 (01): : 1 - 10
[27] THE MULTISET CHROMATIC NUMBER OF A GRAPH
Chartrand, Gary
Okamoto, Futaba
Salehi, Ebrahim
Zhang, Ping
MATHEMATICA BOHEMICA, 2009, 134 (02): : 191 - 209
[28] THE STRONG CHROMATIC NUMBER OF A GRAPH
ALON, N
RANDOM STRUCTURES & ALGORITHMS, 1992, 3 (01) : 1 - 7
[29] Rank and chromatic number of a graph
Kotlov, A
JOURNAL OF GRAPH THEORY, 1997, 26 (01) : 1 - 8
[30] Spectral Inequalities on Independence Number, Chromatic Number, and Total Chromatic Number of a Graph
Li, Rao
JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY, 2015, 18 (1-2): : 41 - 46

← 1 2 3 4 5 →