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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()
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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
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
Keywords:
Ramsey number;  the graph of order six;  three-partite graph
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.

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