Grinstead's conjecture is true for graphs with a small clique number

被引:3
|
作者
Kashiwabara, Kenji
Sakuma, Tadashi
机构
[1] Univ Tokyo, Grad Sch Arts & Sci, Dept Syst Sci, Meguro Ku, Tokyo 1538902, Japan
[2] Yamagata Univ, Fac Educ Art & Sci, Yamagata 9908560, Japan
关键词
circular partitionable graph; CGPW-graph; Grinstead's conjecture;
D O I
10.1016/j.disc.2005.12.040
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We will show that Grinstead's Conjecture holds true if min(alpha(G), omega(G)) <= 8. In other words; a circular partitionable graph G satisfying min(alpha(G), omega(G))<= 8 is always a so-called "CGPW-graph". (c) 2006 Elsevier B.V. All rights reserved.
引用
收藏
页码:2572 / 2581
页数:10
相关论文
共 50 条
  • [1] Dense Graphs with Small Clique Number
    Goddard, Wayne
    Lyle, Jeremy
    JOURNAL OF GRAPH THEORY, 2011, 66 (04) : 319 - 331
  • [2] The list chromatic number of graphs with small clique number
    Molloy, Michael
    JOURNAL OF COMBINATORIAL THEORY SERIES B, 2019, 134 : 264 - 284
  • [3] Ohba's conjecture is true for graphs with independence number at most three
    Shen, Yufa
    He, Wenjie
    Zheng, Guoping
    Li, Yanpo
    APPLIED MATHEMATICS LETTERS, 2009, 22 (06) : 938 - 942
  • [4] New Construction of Graphs with High Chromatic Number and Small Clique Number
    Daneshpajouh, Hamid Reza
    DISCRETE & COMPUTATIONAL GEOMETRY, 2018, 59 (01) : 238 - 245
  • [5] New Construction of Graphs with High Chromatic Number and Small Clique Number
    Hamid Reza Daneshpajouh
    Discrete & Computational Geometry, 2018, 59 : 238 - 245
  • [6] ON THE CONJECTURE OF DIAMETERS OF ITERATED CLIQUE GRAPHS
    刘彦佩
    董峰明
    李祥贵
    Chinese Science Bulletin, 1990, (10) : 874 - 875
  • [7] ON THE CONJECTURE OF DIAMETERS OF ITERATED CLIQUE GRAPHS
    LIU, YP
    DONG, FM
    LI, XG
    CHINESE SCIENCE BULLETIN, 1990, 35 (10): : 874 - 875
  • [8] On clique-inverse graphs of graphs with bounded clique number
    Alcon, Liliana
    Gravier, Sylvain
    Sales, Claudia L.
    Protti, Fabio
    Ravenna, Gabriela
    JOURNAL OF GRAPH THEORY, 2020, 94 (04) : 531 - 538
  • [9] GRAPHS WHOSE CIRCULAR CLIQUE NUMBER EQUAL THE CLIQUE NUMBER
    XU Baogang ZHOU Xinghe School of Mathematics Computer Science Nanjing Normal University Ninghai Road Nanjing China
    Journal of Systems Science and Complexity, 2005, (03) : 340 - 346
  • [10] GRAPHS WHOSE CIRCULAR CLIQUE NUMBER EQUAL THE CLIQUE NUMBER
    XU Baogang ZHOU Xinghe School of Mathematics & Computer Science
    Journal of Systems Science & Complexity, 2005, (03) : 340 - 346