Triangle-free intersection graphs of line segments with large chromatic number

被引：54

作者：

Pawlik, Arkadiusz ^{[1
]}

Kozik, Jakub ^{[1
]}

Krawczyk, Tomasz ^{[1
]}

Lason, Michal ^{[1
,2
]}

Micek, Piotr ^{[1
]}

Trotter, William T. ^{[3
]}

Walczak, Bartosz ^{[1
,4
]}

机构：

[1] Jagiellonian Univ, Fac Math & Comp Sci, Theoret Comp Sci Dept, Krakow, Poland

[2] Polish Acad Sci, Inst Math, Warsaw, Poland

[3] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[4] Ecole Polytech Fed Lausanne, CH-1015 Lausanne, Switzerland

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES B | 2014年 / 105卷

关键词：

Intersection graph; Line segments; Triangle-free; Chromatic number; ARCWISE CONNECTED SETS; PLANE; INTERVALS; RELATIVES;

D O I：

10.1016/j.jctb.2013.11.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the 1970s Erdos asked whether the chromatic number of intersection graphs of line segments in the plane is bounded by a function of their clique number. We show the answer is no. Specifically, for each positive integer k we construct a triangle-free family of line segments in the plane with chromatic number greater than k. Our construction disproves a conjecture of Scott that graphs excluding induced subdivisions of any fixed graph have chromatic number bounded by a function of their clique number. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：6 / 10

页数：5

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