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
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