The Clique Problem in Ray Intersection Graphs

被引：21
|
作者：
Cabello, Sergio [1 ]
Cardinal, Jean [2 ]
Langerman, Stefan [2 ]
机构：
[1] Univ Ljubljana, Dept Math, IMFM, FMF, Ljubljana, Slovenia
[2] Univ Libre Bruxelles, Dept Comp Sci, Brussels, Belgium
来源：
DISCRETE & COMPUTATIONAL GEOMETRY | 2013年 / 50卷 / 03期
关键词：
Geometric intersection graphs; Segment intersection graphs; Maximum clique; NP-hardness;
D O I：
10.1007/s00454-013-9538-5
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Ray intersection graphs are intersection graphs of rays, or halflines, in the plane. We show that any planar graph has an even subdivision whose complement is a ray intersection graph. The construction can be done in polynomial time and implies that finding a maximum clique in a segment intersection graph is NP-hard. This solves a 21-year old open problem posed by Kratochvil and NeetA (TM) il (Comment Math Univ Carolinae 31(1):85-93, 1990).
引用
下载
收藏
页码：771 / 783
页数：13
相关论文
共 50 条
  • [1] The Clique Problem in Ray Intersection Graphs
    Cabello, Sergio
    Cardinal, Jean
    Langerman, Stefan
    ALGORITHMS - ESA 2012, 2012, 7501 : 241 - 252
  • [2] The Clique Problem in Ray Intersection Graphs
    Sergio Cabello
    Jean Cardinal
    Stefan Langerman
    Discrete & Computational Geometry, 2013, 50 : 771 - 783
  • [3] On the clique problem in intersection graphs of ellipses
    Ambühl, C
    Wagner, U
    ALGORITHMS AND COMPUTATION, PROCEEDINGS, 2002, 2518 : 489 - 500
  • [4] The clique problem in intersection graphs of ellipses and triangles
    Ambühl, C
    Wagner, U
    THEORY OF COMPUTING SYSTEMS, 2005, 38 (03) : 279 - 292
  • [5] The Clique Problem in Intersection Graphs of Ellipses and Triangles
    Christoph Ambühl
    Uli Wagner
    Theory of Computing Systems, 2005, 38 : 279 - 292
  • [6] Intersection graphs and the clique operator
    Gutierrez, M
    GRAPHS AND COMBINATORICS, 2001, 17 (02) : 237 - 244
  • [7] Intersection Graphs and the Clique Operator
    Marisa Gutierrez
    Graphs and Combinatorics, 2001, 17 : 237 - 244
  • [8] Clique Chromatic Numbers of Intersection Graphs
    D. A. Zakharov
    A. M. Raigorodskii
    Mathematical Notes, 2019, 105 : 137 - 139
  • [9] Clique Chromatic Numbers of Intersection Graphs
    Zakharov, D. A.
    Raigorodskii, A. M.
    MATHEMATICAL NOTES, 2019, 105 (1-2) : 137 - 139
  • [10] THE CLIQUE PROBLEM FOR PLANAR GRAPHS
    PAPADIMITRIOU, CH
    YANNAKAKIS, M
    INFORMATION PROCESSING LETTERS, 1981, 13 (4-5) : 131 - 133
12345