Triangle-Free Geometric Intersection Graphs with No Large Independent Sets

被引：5
|
作者：
Walczak, Bartosz [1 ]
机构：
[1] Jagiellonian Univ, Fac Math & Comp Sci, Theoret Comp Sci Dept, Krakow, Poland
来源：
DISCRETE & COMPUTATIONAL GEOMETRY | 2015年 / 53卷 / 01期
基金：
瑞士国家科学基金会;
关键词：
Intersection graph; Line segments; Triangle-free; Maximum independent set; Fractional chromatic number; LARGE CHROMATIC NUMBER; PLANE;
D O I：
10.1007/s00454-014-9645-y
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
It is proved that there are triangle-free intersection graphs of line segments in the plane with arbitrarily small ratio between the maximum size of an independent set and the total number of vertices.
引用
收藏
页码：221 / 225
页数：5
相关论文
共 50 条
  • [1] Triangle-Free Geometric Intersection Graphs with No Large Independent Sets
    Bartosz Walczak
    [J]. Discrete & Computational Geometry, 2015, 53 : 221 - 225
  • [2] Triangle-Free Geometric Intersection Graphs with Large Chromatic Number
    Arkadiusz Pawlik
    Jakub Kozik
    Tomasz Krawczyk
    Michał Lasoń
    Piotr Micek
    William T. Trotter
    Bartosz Walczak
    [J]. Discrete & Computational Geometry, 2013, 50 : 714 - 726
  • [3] LARGE INDEPENDENT SETS IN TRIANGLE-FREE PLANAR GRAPHS
    Dvorak, Zdenek
    Mnich, Matthias
    [J]. SIAM JOURNAL ON DISCRETE MATHEMATICS, 2017, 31 (02) : 1355 - 1373
  • [4] Large Independent Sets in Triangle-Free Planar Graphs
    Dvorak, Zdenek
    Mnich, Matthias
    [J]. ALGORITHMS - ESA 2014, 2014, 8737 : 346 - 357
  • [5] Triangle-Free Geometric Intersection Graphs with Large Chromatic Number
    Pawlik, Arkadiusz
    Kozik, Jakub
    Krawczyk, Tomasz
    Lason, Michal
    Micek, Piotr
    Trotter, William T.
    Walczak, Bartosz
    [J]. DISCRETE & COMPUTATIONAL GEOMETRY, 2013, 50 (03) : 714 - 726
  • [6] Independent dominating sets in triangle-free graphs
    Wayne Goddard
    Jeremy Lyle
    [J]. Journal of Combinatorial Optimization, 2012, 23 : 9 - 20
  • [7] Finding independent sets in triangle-free graphs
    Fraughnaugh, K
    Locke, SC
    [J]. SIAM JOURNAL ON DISCRETE MATHEMATICS, 1996, 9 (04) : 674 - 681
  • [8] COUNTING INDEPENDENT SETS IN TRIANGLE-FREE GRAPHS
    Cooper, Jeff
    Mubayi, Dhruv
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 142 (10) : 3325 - 3334
  • [9] Independent dominating sets in triangle-free graphs
    Goddard, Wayne
    Lyle, Jeremy
    [J]. JOURNAL OF COMBINATORIAL OPTIMIZATION, 2012, 23 (01) : 9 - 20
  • [10] THE NUMBER OF MAXIMAL INDEPENDENT SETS IN TRIANGLE-FREE GRAPHS
    HUJTER, M
    TUZA, Z
    [J]. SIAM JOURNAL ON DISCRETE MATHEMATICS, 1993, 6 (02) : 284 - 288
12345