【摘要】 用r种颜色对图G的所有边着色,记着第i色的边构成的子图为Gi,如果存在一种着色方法使得对所有的1≤i≤r都满足Hi Gi,则称图G对于(H1,H2,…,Hr)可r着色.R am sey数R(H1,H2,…,Hr)是使得完全图Kn对于(H1,H2,…,Hr)不可r着色的最小正整数n.令m1>m2≥m3,E r.do.s等给出了当m1足够大时R(Cm1,Cm2,Cm3)的值.通过对m1不是足够大的情况进行研究,证明了当m≥5时,R(Cm,C3,C3)=5m-4;并给出了当m1≤7时R(Cm1,Cm2,Cm3)的值.更多还原

【Abstract】 Let G_i be the subgraph of G whose edges are in the i-th color in an r-coloring of the edges of a graph G.If there exists an r-coloring of the edges of a graph G such that H_iG_i for all 1≤i≤r, then G is said to be r-colorable to（H₁,H₂,…,H_r）.The multicolor Ramsey number R（H₁,H₂,…,H_r） is the smallest integer n such that K_n is not r-colorable to（H₁,H₂,…,H_r）.Let m₁>m₂≥m₃.If m₁ is sufficiently large,Erdo··s,et al.determined the values of R(C_m1,C_m2, C_m3).The case that m₁ is not sufficiently large is studied.It is proved that R（C_m,C₃,C₃）=5m-4 for m≥5,the values of R(C_m1,C_m2,C_m3) for m₁≤7 are determined.更多还原