SMALL ON-LINE RAMSEY NUMBERS - A NEW APPROACH

被引：0
|
作者：
Gordinowicz, Przemyslaw [1 ]
Pralat, Pawel [2 ]
机构：
[1] Lodz Univ Technol, Inst Math, Lodz, Poland
[2] Ryerson Univ, Dept Math, Toronto, ON M5B 2K3, Canada
来源：
CONTRIBUTIONS TO DISCRETE MATHEMATICS | 2018年 / 13卷 / 02期
基金：
加拿大自然科学与工程研究理事会;
关键词：
on-line Ramsey number; size Ramsey number; PATHS; GAMES;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this note, we revisit the problem of calculating small on-line Ramsey numbers (R) over bar (G, H). A new approach is proposed that reduces the running time of the algorithm determining that (R) over bar (K-3, K-4) = 17 by a factor of at least 2 . 10(6) compared to the previously used approach. Using high performance computing networks, we determined that (R) over bar (K-4, K-4) >= 26, (R) over bar (K-3, K-5) >= 25, and that (K-3, K-3, K-3) >= 20 for a natural generalization to three colours. All graphs on 3 or 4 vertices are investigated as well, including nonsymmetric cases.
引用
收藏
页码：101 / 111
页数：11
相关论文
共 50 条
  • [41] NARROWING DOWN ON THE NEW RAMSEY NUMBERS
    MILLS, G
    JOURNAL OF SYMBOLIC LOGIC, 1979, 44 (03) : 476 - 476
  • [42] A new view of bipartite Ramsey numbers
    Bi, Zhenming
    Chartrand, Gary
    Zhang, Ping
    Journal of Combinatorial Mathematics and Combinatorial Computing, 2019, 108 : 193 - 203
  • [43] NEW RESULTS ON GENERALIZED RAMSEY NUMBERS
    HADDAD, L
    SABBAGH, G
    COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1969, 268 (25): : 1516 - &
  • [44] New upper bounds for Ramsey numbers
    Ru, HY
    Min, ZK
    EUROPEAN JOURNAL OF COMBINATORICS, 1998, 19 (03) : 391 - 394
  • [45] Ramsey numbers for small graphs versus small disconnected graphs
    Lortz, Roland
    Mengersen, Ingrid
    AUSTRALASIAN JOURNAL OF COMBINATORICS, 2011, 51 : 89 - 108
  • [46] Coloring number and on-line Ramsey theory for graphs and hypergraphs
    H. A. Kierstead
    Goran Konjevod
    Combinatorica, 2009, 29 : 49 - 64
  • [47] COLORING NUMBER AND ON-LINE RAMSEY THEORY FOR GRAPHS AND HYPERGRAPHS
    Kierstead, H. A.
    Konjevod, Goran
    COMBINATORICA, 2009, 29 (01) : 49 - 64
  • [48] On-line hemofiltration - Old concept - New approach
    Ledebo, I
    HEMODIALYSIS TECHNOLOGY, 2002, 137 : 221 - 226
  • [49] A new approach for on-line optimisation of a fuzzy controller
    Haggege, J
    Benrejeb, M
    Borne, P
    ICECS 2001: 8TH IEEE INTERNATIONAL CONFERENCE ON ELECTRONICS, CIRCUITS AND SYSTEMS, VOLS I-III, CONFERENCE PROCEEDINGS, 2001, : 971 - 975
  • [50] A new approach to the on-line monitoring of cutting chatter
    Fu, LY
    Shi, HY
    Yu, JY
    PROGRESS OF MACHINING TECHNOLOGY: WITH SOME TOPICS IN ADVANCED MANUFACTURING TECHNOLOGY, 2000, : 606 - 610
12345