THE CYCLE-COMPLETE GRAPH RAMSEY NUMBERS R(Cn, K8), FOR 10 ≤ n ≤ 15

被引：1

作者：

Baniabedalruhman, A. ^{[1
]}

机构：

[1] Yarmouk Univ, Dept Math, Irbid, Jordan

来源：

JORDAN JOURNAL OF MATHEMATICS AND STATISTICS | 2023年 / 16卷 / 04期

关键词：

Ramsey number; cycle graph; complete graph;

D O I：

10.47013/16.4.6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given two graphs H-1 and H-2, the Ramsey number R(H-1, H-2) is the smallest natural number n such that each graph of order n contains a copy of H-1 or its complement contains a copy of H-2. In this paper, we find the exact Ramsey number R(C-n, K-8) for 10 <= n <= 15, where C-n is the cycle on n vertices and K8 is the complete graph of order 8.

引用

页码：703 / 718

页数：16

共 13 条

[1]

Baniabedalruhman A., 2006, M.Sc. Thesis

[2]

Baniabedalruhman A., 2010, Journal of Combinatorics, Information System Sciences, V35, P293

[3]

Bataineh M. S. A., 2011, The Cycle-Complete Graph Ramsey Number r(C9, K8)

[4]

Bollobas B., 2000, AUSTRALAS J COMB, V22, P63

[5]

BONDY JA, 1973, J COMB THEORY B, V14, P46, DOI DOI 10.1016/J.JCTB.2008.12.002

[6] The Ramsey numbers R(Cm, K7) and R(C7, K8) [J].

Chen, Yaojun ;

Cheng, T. C. Edwin ;

Zhang, Yunqing .

EUROPEAN JOURNAL OF COMBINATORICS, 2008, 29 (05) :1337-1352

[7]

Erdos P., 1978, Journal of Graph Theory, V2, P53

[8]

Faudree R. J., 1974, Discrete Mathematics, V8, P313, DOI 10.1016/0012-365X(74)90151-4

[9]

Jaradat M. M. M., 2007, SUT Journal of Mathematics, V43, P85

[10] On a problem of formal logic [J].

Ramsey, FP .

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1930, 30 :264-286

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