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[1] Gu Hua, Song Hongxue, Liu Xiangyang,. Ramsey numbers r(K1, 4, G)for all three-partite graphs G of order six [J]. Journal of Southeast University (English Edition), 2004, 20 (3): 378-380. [doi:10.3969/j.issn.1003-7985.2004.03.023]
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Ramsey numbers r(K1, 4, G)for all three-partite graphs G of order six()
K1, 4和六阶三部图的Ramsey数r(K1, 4, G)
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
20
Issue:
2004 3
Page:
378-380
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2004-09-30

Info

Title:
Ramsey numbers r(K1, 4, G)for all three-partite graphs G of order six
K1, 4和六阶三部图的Ramsey数r(K1, 4, G)
Author(s):
Gu Hua1;  Song Hongxue2;  Liu Xiangyang1
1College of Science, Hohai University, Nanjing 210098, China
2Department of Mathematics and Physics, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
顾华1;  宋洪雪2;  刘向阳1
1河海大学理学院, 南京 210098; 2南京邮电学院应用数理系, 南京 210003
Keywords:
Ramsey number;  the graph of order six;  three-partite graph
Ramsey数;  六阶图;  三部图
PACS:
O157.5
DOI:
10.3969/j.issn.1003-7985.2004.03.023
Abstract:
In this paper, we use a combinatorial analysis method. In the complete graph KN with edges colored arbitrarily by red or blue, we consider the proposition of the subgraph of the red graph or blue graph induced by the neighborhood of some vertex in V(KN). Inspired by the main results of Jayawardene and Rousseau(Ars Combinatoria, 2000, 163-173), we determine the Ramsey numbers of r(K1, 4, G), where G is the three-partite graph of order six without isolate vertex.
本文主要应用了组合分析的方法. 在对所有边任意地进行了红、蓝2种颜色着色的完全图KN中, 考察了完全图KN的顶点集中某点的邻域在红图或蓝图中所生成的子图的性质. 在Jayawardene和Rousseau(Ars Combinatoria, 2000, 163-173)的主要结果的启发下, 研究并确定了另一种常见的五阶图K1, 4对于所有无孤立点的六阶三部图G的Ramsey数r(K1, 4, G).

References:

[1] Bollobás Béla. Modern graph theory[M]. New York: Springer, 2001. 1-28.
[2] Jayawardene C J, Rousseau C C. Ramsey numbers r(C5, G)5 for all graphs G of order six [J]. Ars Combinatoria, 2000, 57: 163-173.
[3] Xu Junming. Graph and its applications[M]. Hefei: University of Science and Technology of China Press, 1998. 8-18.(in Chinese)
[4] Rousseau C C, Sheehan J. A class of Ramsey problems involving trees[J]. Journal of the Lonmathematical Society(2), 1978, 18: 392-396.
[5] Hendry George R T. Ramsey numbers for graphs with five vertices[J]. Journal of Graph Theory, 1989, 13: 245-248.

Memo

Memo:
Biography: Gu Hua(1977—), female, master, lecturer, guhuasy@163.com.
Last Update: 2004-09-20