Abstract: The Ramsey number n=R(G,H) has been defined as the minimum n such that every 2-coloring (red and green) of the edges of the complete graph K_n has a red subgraph G, or a green subgraph H.By constructing cyclic colorings systematically with the help of a microcomputer, it is proved that
R(K₃,K₁₁-e)>=42, R(K₃,K₁₃-e)>=54,
R(K₃,K₁₄-e)>=59, R(K₃,K₁₅-e)>=69.

Key words: Ramsey number, lower bound, cyclic coloring

摘要： 利用一种系统地构造循环着色的算法，借助计算机证明了Ramsey数R(K₃,K_q-e) 的下述新下界：
R(K₃,K₁₁-e)≥42, R(K₃,K₁₃-e)≥54,
R(K₃,K₁₄-e)≥59, R(K₃,K₁₅-e)≥69。

关键词: Ramsey数, 下界, 循环着色