摘要
n个顶点的完全图K_s,其边着色红或蓝,得K_n的二色图.当二色图既不包含蓝色团K_s,又不包含红色团K_y,则记作K_n(3,p).如果把K_n(3,p)成立的最大n值记为R(3,p),那未形如K_(n(3,p)(3,p)的一系列二色图与形为r(3,p)的一系列Ramsey数相关,已知R(3,p)=r(3,p)-1[1].本文讨论两个问题:(1)当p≤7时,给出二色图K_(R(3,p))(3,p)的递增性质,即K_(R(3,p))(3,p)可在K_(R(3,p-1))(3,p-1)上生成;(2)在二色图K_(22)(3,7)上生成K_(27)(3,8).从而知R(3,8)≥27,随知Ramsey数r(3,8)≥28.
Let K_n be the complete graph of order n.If red and blue are assigned to the edges of K_n such that there is neither subgraph K_3 whose edges are all blue or subgraph K,whose edges are all red,then such a 2-edge-chromatic K_n is denoted by K_n(3,p).Denote the maximum value of n for K_n(3,p) as R(3,p), then obviously R(3,p)=r(3,p)-1,where r(3,p) is the Ramsey number.We obtain two results:(1) When p≤7,we show that K_(R(3,p))(3,p) can be constructed on the basis of K_(R(3,p-1))(3,p-1);(2)K_(27)(3, 8) is obtained by K_(22)(3,7),hence R(3,8)≥27,and so r(3,8)≥28.
出处
《内蒙古大学学报（自然科学版）》
CAS
CSCD
1992年第2期157-162,共6页
Journal of Inner Mongolia University：Natural Science Edition
