独立数的一个下界

设G是一个图,其度序列为(d_v). 若由G的任意邻域导出子图的最大度至多为m, 则G的独立数至少是 ,这里当x>0, 函数f_m+1(x)大于 . 对于加权图G=(V,E,w), 证明了它的加权独立数至少是 ,这里w_v是顶点v的权重.     

Ramsey函数估值和图论中的渐近方法

本文介绍在图论极值问题Ramsey数的渐近性态研究上的一些成果,它们的背景和所使用的证明方法,主要是随机图方法和分析方法,给出了几个体现其特色,简单易懂但不失严格性的证明。我们还简介了近年来几项重要数学奖项,包括1997年Fulkerson奖,1998年Fields奖和1999年Wolf奖得主与Ramsey理论有关的工作和方法。这些方法正改变着极值图论研究的面貌,它们将给这个领域带来新的景象。本文也包含笔者的一些结果。     

Ramsey Number With Largen

This is an announcement that r(C2m+1, Kn) ≤ c(m) has been proved. The Rarnsey number r(H, Kn) is the smallest integer N such that every H-free graph on N vertices has independence number at least n. The study of Ramsey number r(Ck, Kn) was initiated by Bondy and Erdos[2]. They proved that for any fixed n, r(Ck, Kn) = (k - 1)(n - 1) + 1if k≥n2-1, and r(Ck, Kn)≤kn2. For fixed k≥3, it is difficult to obtain a satisfied bound of r(Ck,Kn) for n →∞. The bound of Bondy and Erdos was improved as r(Ck, Kn)≤c(k)n1+1/m,where m = [(k - 1)/2] by Erdos, Faudree, Rousseau and Schelp[4]. For even cycle, a more refined     

Ramsey Number r(C_(2m 1), K_n) With Large n

This is an announcement that r(C2m 1, Kn) ＜ c(m) ( ) 1/m has been proved.The Ramsey number r(H, Kn) is the smallest integer N such that every H-free graph onN vertices has independence number at least n. The study of Ramsey number r(Ck, Kn) wasinitiated by Bondy and Erd s[2]. They proved that for any fixed n, r(Ck, Kn) = (k - 1)(n - 1) 1if k n2 - 1, and r(Ck, Kn) kn2. For fixed k 3, it is difficult to obtain a satisfied bound ofr(Ck, Kn) for n → ∞ . The bound of Bondy and Erd s w…