零和Ramsey数R(C_3,Z_3)的下界——(3)

The Lower Bound of the Zero-Sum Ramsey Number R(C_3,Z_3)—(3)

Bialostocki和Dierker给出了古典Ramaey定理下列有趣的推广:设G是一个有m条边的图,整数k≥2,且k|m,Z_k表示k阶循环群。定义R(G,Z_k)表示一个极小整数t,使得对K_t的边的任意Z_k—染色(即一个泛函C:E(K_t)→Z_k),K_t中都存在一个同构于G的子图具有下列性质 sum from e∈E(G) C(e)≡0(mod k)。本文证明R(C_3,Z_3)≥11。

Bialostocki and Dierker raised the following interesting variant of the classical Ramse Theorem:Let G be a graph having m edges and let k≥2 be an integer such that k|m, and let Z_4 be the cyclic group of order k. Define R(G,Z,) to be the minimal integer t such that for every Z_4—coloring of the edges of K,, i.e. , a function c: E(K_4)→Z_k, there is in K_i a copy of G with the property that c(e)≡0(mod k).They proved that Zhao Dongfang and Gen Zhibin proved that R(C_3,Z_3)≥8.Zhao Dongfang proved that R(C_3,Z_3)≥9.In this paper, we proved that R(C_3,Z_3)≥11.