STRING GRAPHS .1. THE NUMBER OF CRITICAL NONSTRING GRAPHS IS INFINITE

被引：35
|
作者：
KRATOCHVIL, J
机构：
[1] Department of Algebra, Faculty of Mathematics and Physics, Charles University
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES B | 1991年 / 52卷 / 01期
关键词：
D O I：
10.1016/0095-8956(91)90090-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
String graphs (intersection graphs of curves in the plane) were originally studied in connection with RC-circuits. The family of string graphs is closed in the induced minor order, and so it is reasonable to study critical nonstring graphs (nonstring graphs such that all of their proper induced minors are string graphs). The question of whether there are infinitely many nonisomorphic critical nonstring graphs has been an open problem for some time. The main result of this paper settles this question. In a later paper of this series we show that recognizing string graphs is NP-hard. © 1991.
引用
收藏
页码：53 / 66
页数：14
相关论文
共 50 条
  • [1] The Colouring Number of Infinite Graphs
    Bowler, Nathan
    Carmesin, Johannes
    Komjath, Peter
    Reiher, Christian
    [J]. COMBINATORICA, 2019, 39 (06) : 1225 - 1235
  • [2] The Colouring Number of Infinite Graphs
    Nathan Bowler
    Johannes Carmesin
    Péter Komjáth
    Christian Reiher
    [J]. Combinatorica, 2019, 39 : 1225 - 1235
  • [3] Critical and infinite directed graphs
    Boudabbous, Imed
    Ille, Pierre
    [J]. DISCRETE MATHEMATICS, 2007, 307 (19-20) : 2415 - 2428
  • [4] TOPOLOGICAL ASPECTS OF SEPARATION IN INFINITE GRAPHS .1.
    POLAT, N
    [J]. MATHEMATISCHE ZEITSCHRIFT, 1979, 165 (01) : 73 - 100
  • [5] String Graphs with Precise Number of Intersections
    Chmel, Petr
    Jelinek, Vit
    [J]. GRAPH DRAWING AND NETWORK VISUALIZATION, GD 2023, PT I, 2023, 14465 : 78 - 92
  • [6] INFINITE FAMILIES OF CROSSING-CRITICAL GRAPHS WITH A GIVEN CROSSING NUMBER
    SIRAN, J
    [J]. DISCRETE MATHEMATICS, 1984, 48 (01) : 129 - 132
  • [7] THE ULAM NUMBER OF INFINITE-GRAPHS
    CHILAKAMARRI, KB
    DEAN, N
    [J]. GRAPHS AND COMBINATORICS, 1995, 11 (02) : 109 - 120
  • [8] ON THE HADWIGER NUMBER OF INFINITE-GRAPHS
    SEIFTER, N
    [J]. ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 1992, 62 : 207 - 215
  • [9] INFINITE GRAPHS WITH A SPECIFIED NUMBER OF COLORINGS
    HECHLER, SH
    [J]. DISCRETE MATHEMATICS, 1977, 19 (03) : 241 - 255
  • [10] The chromatic number of infinite graphs - A survey
    Peter Komjath
    [J]. DISCRETE MATHEMATICS, 2011, 311 (15) : 1448 - 1450
12345