Generalised Ramsey numbers with respect to classes of graphs

被引:0
|
作者
Cockayne, EJ [1 ]
Favaron, O [1 ]
Grobler, PJP [1 ]
Mynhardt, CM [1 ]
Puech, J [1 ]
机构
[1] Univ Victoria, Dept Math, Victoria, BC, Canada
关键词
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let H-1, ..., H-t be classes of graphs. The class Ramsey number R(H-1 ,...,H-t) is the smallest integer n such that for each t-edge colouring (G(1), ..., G(t)) of K-n, there is at least one i is an element of {1, ..., t} such that Gi contains a subgraph H-i is an element of H-i. We take t = 2 and determine R(G(l)(1), G(m)(1)) for all 2 less than or equal to l less than or equal to m and R(G(l)(2), G(m)(2)) for all 3 less than or equal to l less than or equal to m, where G(j)(i) consists of all edge-minimal graphs of order j and minimum degree i.
引用
收藏
页码:279 / 288
页数:10
相关论文
共 50 条
  • [1] CHROMATIC RAMSEY NUMBERS OF GENERALISED MYCIELSKI GRAPHS
    Tardif, Claude
    [J]. DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2024, 44 (04) : 1327 - 1339
  • [2] On the Ramsey numbers for the tree graphs versus certain generalised wheel graphs
    Chng, Zhi Yee
    Tan, Ta Sheng
    Wong, Kok Bin
    [J]. DISCRETE MATHEMATICS, 2021, 344 (08)
  • [3] Ramsey and Gallai-Ramsey Numbers for Two Classes of Unicyclic Graphs
    Wang, Zhao
    Mao, Yaping
    Magnant, Colton
    Zou, Jinyu
    [J]. GRAPHS AND COMBINATORICS, 2021, 37 (01) : 337 - 354
  • [4] Ramsey and Gallai-Ramsey Numbers for Two Classes of Unicyclic Graphs
    Zhao Wang
    Yaping Mao
    Colton Magnant
    Jinyu Zou
    [J]. Graphs and Combinatorics, 2021, 37 : 337 - 354
  • [5] COMPLEMENTARY RAMSEY NUMBERS AND RAMSEY GRAPHS
    Munemasa, Akihiro
    Shinohara, Masashi
    [J]. JOURNAL OF THE INDONESIAN MATHEMATICAL SOCIETY, 2019, 25 (02) : 146 - 153
  • [6] Graph classes and Ramsey numbers
    Belmonte, Remy
    Heggernes, Pinar
    van 't Hof, Pim
    Rafiey, Arash
    Saei, Reza
    [J]. DISCRETE APPLIED MATHEMATICS, 2014, 173 : 16 - 27
  • [7] Classes of graphs that are not vertex Ramsey
    Kierstead, HA
    [J]. SIAM JOURNAL ON DISCRETE MATHEMATICS, 1997, 10 (03) : 373 - 380
  • [8] On graphs with linear Ramsey numbers
    Graham, RL
    Rödl, V
    Rucinski, A
    [J]. JOURNAL OF GRAPH THEORY, 2000, 35 (03) : 176 - 192
  • [9] On pattern Ramsey numbers of graphs
    Jamison, RE
    West, DB
    [J]. GRAPHS AND COMBINATORICS, 2004, 20 (03) : 333 - 339
  • [10] ON IRREDUNDANT RAMSEY NUMBERS FOR GRAPHS
    HATTINGH, JH
    [J]. JOURNAL OF GRAPH THEORY, 1990, 14 (04) : 437 - 441