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
  • [41] ON THE SPECTRAL MOMENT OF GRAPHS WITH GIVEN CLIQUE NUMBER
    Li, Shuchao
    Hu, Shuna
    ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2016, 46 (01) : 261 - 282
  • [42] Relative clique number of planar signed graphs
    Das, Sandip
    Ghosh, Prantar
    Prabhu, Swathy
    Sen, Sagnik
    DISCRETE APPLIED MATHEMATICS, 2020, 280 : 86 - 92
  • [43] Clique-transversal number in cubic graphs
    Shan, Erfang
    Zuosong, Liang
    Cheng, T.C.E.
    Discrete Mathematics and Theoretical Computer Science, 2008, 10 (02): : 115 - 124
  • [44] ON THE COP NUMBER AND THE WEAK MEYNIEL'S CONJECTURE FOR ALGEBRAIC GRAPHS
    Biswas, Arindam
    Saha, Jyoti Prakash
    arXiv, 2023,
  • [45] The bondage number of graphs on topological surfaces and Teschner's conjecture
    Gagarin, Andrei
    Zverovich, Vadim
    DISCRETE MATHEMATICS, 2013, 313 (06) : 796 - 808
  • [46] On Tuza's Conjecture for Triangulations and Graphs with Small Treewidth
    Botler, F.
    Fernandes, C. G.
    Gutierrez, J.
    ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE, 2019, 346 : 171 - 183
  • [47] On Tuza's conjecture for triangulations and graphs with small treewidth
    Botler, Fabio
    Fernandes, Cristina G.
    Gutierrez, Juan
    DISCRETE MATHEMATICS, 2021, 344 (04)
  • [48] The jump of the clique chromatic number of random graphs
    Lichev, Lyuben
    Mitsche, Dieter
    Warnke, Lutz
    RANDOM STRUCTURES & ALGORITHMS, 2023, 62 (04) : 1016 - 1034
  • [49] THE CLIQUE MINOR OF GRAPHS WITH INDEPENDENCE NUMBER TWO
    Pang, Shiyou
    Miao, Lianying
    Sun, Qingbo
    Miao, Zhengke
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2009, 1 (01) : 121 - 125
  • [50] The Zagreb indices of graphs with a given clique number
    Xu, Kexiang
    APPLIED MATHEMATICS LETTERS, 2011, 24 (06) : 1026 - 1030