林启忠;杜智华;

• 1:福州大学数学与计算机科学学院
• 2:新疆师范大学数学科学学院

摘要(Abstract)：

设多色二部Ramsey数brk(C6;Kn,n)是最小的正整数N使得对二部完全图KN,N的边进行k+1着色时,总存在前k色中某种单色的C6或者第k+1色的Kn,n.本文主要利用随机方法得到brk(C6;Kn,n)=Θlong33//22 n对k≥3都成立,并且得到br2(C6;Kn,n)≥c(nlolgoglo3g nn)3/2对充分大的n成立.

关键词(KeyWords)： 二部Ramsey数;圈;渐进阶

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金青年项目(11101086);; 福建省教育厅科技项目(JK2010007)

作者(Author): 林启忠;杜智华;

Email:

DOI:

参考文献(References)：

• [1]Thomason A.On finite Ramsey numbers[J].Europ J Combin,1982,3:263-273.
• [2]Conlon D.A new upper bound for the bipartite Ramsey problem[J],J Graph Theory,2008,58:351-356.
• [3]Li Y,Tang X,Zang W.Ramsey functions involving Km,n with n large[J].Discrete Math,2005,300:120-128.
• [4]Caro Y,Rousseau C.Asymptotic bounds for bipartite Ramsey numbers[J].Electronic J Combin,2001,8(1):R17.
• [5]Lin Q,Li Y.Bipartite ramsey numbers involving large Kn,n[J].European J Combin,2009,30:923-928.
• [6]Alon N,R¨odl V.Sharp bounds for some multicolor Ramsey numbers[J].Combinatorics,2005,25:125-141.
• [7]Lin Q,Li Y.Multicolor Bipartite Ramsey Number of C4and large Kn,n[J].J Graph Theory,2011,67:47-54.
• [8]Bohman T,Keevash P.The early evolution of H-free process[J].Invent Math,2010,181:291-336.
• [9]Spencer J.Asymptotic lower bounds for Ramsey functions[J],Discrete Math,1977,20:69-76.
• [10]Kim J H.The Ramsey number R(3,t)has order of magnitude t2/log t[J].Random Structures Algorithms,1995,7:173-207.
• [11]Bohman T.The triangle-free process[J].Advances in Math,2009,221:1653-1677.
• [12]Erdo s P,Faudree R,Rousseau C,et al.A Ramsey Problem of Harary on graphs with prescribed size[J].Discrete Math,1987,67:227-233.
• [13]Krivelevich M.Bounding Ramsey numbers through large deviation inequalities[J].Random Struct Algo,1995,7:145-155.
• [14]Li Y,Zang W.Ramsey numbers involving large dense graphs and bipartite Turan numbers[J].J Combin Theory Ser B,2003,87:280-288.
• [15]Dong L,Li Y,Lin Q.Ramsey numbers involving graphs with large degrees[J].Applied Math Letters,2009,22:1577-1580.
• [16]Erdo s P.Extremal problems in graph theory,in Theory of Graphs and Its Applications(M.Fiedler ed.)(Proc.Symp.Smolenice,1963),New York:Academic Press,29-36.
• [17]Bondy J,Simonovits M.Cycles of even length in graphs[J].J Combin Theory Ser B,1974,16:97-105.
• [18]K¨ova′ri T,S′os T,Tura′n P.On a problem of K.Zarankiewicz[J].Colloq Math,1954,3:50-57.
• [19]Fu¨redi Z.An upper bound on Zarankiewicz’problem[J].Combin Probab Comput,1996,5:29-33.
• [20]Brouwer A E,Cohen A M,Neumaier A.Distance-Regular Graphs,Springer-Verlag[M].Berlin,1989.
• [21]Laze F bnik,Ustime nko V A,Woldar A J.Polarities and2k-cycle-free graphs[J].Discrete Math,1999,197/198:503-513.
• [22]Tanner R M.Explicit concentrators from generalized N-gons[J].SIAM J Algebraic Discrete Methods,1984,5:287-293.