Some three-color Ramsey numbers, R(P4, P5, Ck) and R(P4, P6, Ck)

被引：7
|
作者：
Shao, Zehui [1 ]
Xu, Xiaodong [2 ]
Shi, Xiaolong [1 ]
Pan, Linqiang [1 ]
机构：
[1] Huazhong Univ Sci & Technol, Dept Control Sci & Engn, Key Lab Image Proc & Intelligent Control, Wuhan 430074, Peoples R China
[2] Guangxi Acad Sci, Nanning 530007, Guangxi, Peoples R China
来源：
EUROPEAN JOURNAL OF COMBINATORICS | 2009年 / 30卷 / 02期
基金：
中国国家自然科学基金;
关键词：
GRAPHS;
D O I：
10.1016/j.ejc.2008.05.008
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For given graphs G(1), G(2), G(3), the three-color Ramsey number R(G(1), G(2), G(3)) is defined to be the least positive integer n such that every 3-coloring of the edges of complete graph K-n contains a monochromatic copy of G(i) colored with i. for some 1 <= i <= 3. In this paper, we prove that R(P-4, P-5, C-3) = 11, R(P-4, P-5, C-4) = 7, R(P-4, P-5, C-5) = 11, R(P-4, P-5, C-7) = 11, R(P-4, P-5, C-k) = k + 2 for k >= 23; R(P-4, P-6, C-4) = 8, R(P-4, P-6, C-3) = R(P-4, P-6, C-5) = R(P-4, P-6, C-7) = 13, R(P-4, P-6, C-k) = k + 3 for k >= 18. (C) 2008 Elsevier Ltd. All rights reserved.
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页码：396 / 403
页数：8
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