关于Ramsey问题的两个平均值定理及其应用初探

Two Average Value Theorems On Ramsey Problem and the Initial Exploration of Their Applications

本文给出了两个Ｒａｍｓｅｙ数的平均值定理且初步探讨了它们的应用：证明了由此二定理可得Ｒ（３，５）≤１４，Ｒ（ｎ，ｎ）≤Ｒ（ｎ－２，ｎ）＋３Ｒ（ｎ—１，ｎ—１）－１以及当Ｐ＞４５时（５，５，Ｐ）图必含（３，５，１１）子图等性质，本文指出，寻找出Ｒａｍｓｅｙ数Ｒ（ｍ，ｎ）的极图中某类特殊子图是个关键．

In this paper, We give two average value theorems, and initially.explore their applications.We prove R(3,5)≤ 14, R(n,n)≤ R(n-2,n)+3R(n-1,n1)-1 and some Properties such as every(5,5)-graph must contain a (3,5, 11)-graph as its subgraph, when p >45. Perhaps, searching aspecial subgraph is the key for finding the extremal r(m, n)-graph