|Table of Contents|

[1] Song Hongxue,. Asymptotic upper bounds for wheel:complete graph Ramsey numbers [J]. Journal of Southeast University (English Edition), 2004, 20 (1): 126-129. [doi:10.3969/j.issn.1003-7985.2004.01.026]
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Asymptotic upper bounds for wheel:complete graph Ramsey numbers()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
20
Issue:
2004 1
Page:
126-129
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2004-03-30

Info

Title:
Asymptotic upper bounds for wheel:complete graph Ramsey numbers
Author(s):
Song Hongxue
College of Sciences, Hohai University, Nanjing 210098, China
Keywords:
Ramsey numbers;  wheels;  independent number;  complete graphs
PACS:
O29
DOI:
10.3969/j.issn.1003-7985.2004.01.026
Abstract:
It is shown that r(Wm, Kn)≤(1+o(1))C1(n/(logn))</sup>(2m-2)/(m-2) for fixed even m≥4 and n→∞, and r(Wm, Kn)≤(1+o(1))C2((n(2m)/(m+1))/(logn))</sup>(m+1)/(m-1) for fixed odd m≥5 and n→∞, where C1=C1(m)&gt;0 and C2=C2(m)&gt;0, in particular, C2=12 if m=5. It is obtained by the analytic method and using the function fm(x)=∫10((1-t)<sup>1/mdt)/(m+(x-m)t), x≥0, m≥1 on the base of the asymptotic upper bounds for r(Cm, Kn) which were given by Caro, et al. Also, c(n/(logn))5/2≤r(K4, Kn)≤(1+o(1))(n3)/((logn)2)(as n→∞). Moreover, we give r(Kk+Cm, Kn)≤(1+o(1))C5(m)(n/(logn))</sup>k+m/(m-2) for fixed even m≥4 and r(Kk+Cm, Kn)≤(1+o(1))C6(m)((n</sup>(2+(k+1)(m-1))/(2+k(m-1)))/(logn))</sup>k+2/(m-1) for fixed odd m≥3(as n→∞).

References:

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[4] Caro Yair, Li Yusheng, Rousseau C C, et al. Asymptotic bounds for some bipartite graph: complete graph Ramsey numbers [J]. Discrete Mathematics, 2000, 220(2): 51-56.
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[6] Kim J H. The Ramsey number r(3, t) has order of magnitude t2/2logt [J]. Random Structure and Algorithms, 1995, 7: 173-207.
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[9] Li Yusheng, Rousseau C C, Zang Wenan. Asymptotic upper bounds for Ramsey functions [J]. Graph and Combinatorics, 2001, 17: 123-128.

Memo

Memo:
Biography: Song Hongxue(1977—), female, graduate, songhongxue@sohu.com.
Last Update: 2004-03-20