9个经典Ramsey数R(3,t)的新下界

摘要

In the paper, we study the lower bounds for classical Ramsey number R(3, t). By using the property of cyclic graphs of prime order, the methods of computing clique numbers for cyclic graphs of general order are improved. New lower bounds for 9 classical Ramsey numbers are obtained: R(3,29)≥ 183, R(3,30)≥ 189, R(3,32)≥ 213, R(3,33)≥ 218, R(3,34)≥ 226,R(3, 35)≥ 231, R(3, 36)≥ 239, R(3,37)≥ 244, R(3,38)≥ 256, where the first 3 results improve their corresponding best known lower bounds and the remaining 6 results are first reported in this article.%本文研究了经典Ramsey数R(3,t)的下界问题.利用素数阶循环图的性质改进一般阶循环图团数的计算方法,获得了9个经典Ramsey数R(3,t)的新下界:R(3,29)≥183,R(3,30)≥189,R(3,32)≥ 213,R(3,33)≥218,R(3,34)≥226,R(3,35)≥231,R(3,36)≥239,R(3,37)≥244,R(3,38)≥256,其中前三个结果分别改进了迄今已知的最好的下界,后6个结果是本文首次报道的.