Asymptotic upper bounds for K-1,K-m,K-k: complete graph Ramsey Numbers

作者：Song, Hongxue^*

来源：Ars Combinatoria, 2013, 111: 137-144.

• Ramsey numbers
• Bipartite graphs
• Independent number
• Complete graphs
• Join

It is shown that r(K-1,K-m,K-k, K-n) <= (k - 1 + o(1)) (n/log n)(m+1) for any two fixed integers k >= m >= 2 and n -> infinity. It is obtained by the analytic method and using the function f(m) (x) = integral(1)(0) (1-t)(1/m)dt/m+(x-m)t, x >= 0, m >= 1 on the base of the upper bounds for r(K-m,K-k, K-n) which were given by Y. Li and W. Zang. Also, (c - o(1)) (n/log n)(7/3) <= r(W-4, K-n) <= (1 + o(1)) (n/log n)(3) (as n -> infinity). Moreover, we give r(K-l + K-m,K-k, K-n) <= (k - 1 + o(1)) (n/log n)(l+m) for any two fixed integers k >= m >= 2(as n -> infinity).

• 出版日期2013-7
• 单位南京邮电大学; 河海大学