Ramsey数的新上界公式

A New Upper Bound Formula of Ramsey Numbers

对著名的组合数学问题——Ramsey数问题进行了研究,利用Ramsey数的有关性质和归纳法,得到并证明了Ramsey数的一个新上界公式,即N(q_1,q_2,…,q_t;2)≤(q_1+q_2+…+q_t-2t+2)!/[(q_1-1)!(q_2-1)!(q_3-2)!…(q_t-2)!],这个新的上界公式改进了几十年来组合数学和图论方面的专著和教科书中的相应结论,它对计算具体的Ramsey数值很有意义.

Ramsey numbers are of great significance in combinatorial mathematics, but so far people do not know much about them. Using some of their properties and the induction principle, we obtain and prove a new upper bound formula of Ramsey numbers, that is N(q1,q2,…,qt;2)≤(q1+q2+…+q1 - 2t + 2)! /[(q1-1)! (q2-1)!(q3-2)! …(qt-2)!]. It improvesthe relative result in the references of this paper.