论文标题
Ramsey-Turán的独立数量很小的问题
Ramsey-Turán Problems with small independence numbers
论文作者
论文摘要
给定图形$ h $和一个函数$ f（n）$，ramsey-turán编号$ rt（n，h，f（n））$是$ n $ vertex $ h $ h $ h $ h $ - 最多具有独立数字的最大边数，最多是$ f（n）$。对于$ h $是一个小集团，已知许多大约$ rt（n，h，f（n））$的结果，我们将注意力集中在$ h = k_s $上，以$ s \ s \ leq 13 $。通过应用Szemerédi的规律性引理，依赖的随机选择方法和一些加权的Turán-Type结果，我们证明这些集团在$ f（n）$ ah围绕off-diagonal ramsey ramsey nubl $ k_r $ k_r $ k_r $ k_n $ k_ $ k_n $的$ k_n $ s $ rq for的$ k_r $ r c s of for的$ k_r $ r r f for pef的us f（
Given a graph $H$ and a function $f(n)$, the Ramsey-Turán number $RT(n,H,f(n))$ is the maximum number of edges in an $n$-vertex $H$-free graph with independence number at most $f(n)$. For $H$ being a small clique, many results about $RT(n,H,f(n))$ are known and we focus our attention on $H=K_s$ for $s\leq 13$. By applying Szemerédi's Regularity Lemma, the dependent random choice method and some weighted Turán-type results, we prove that these cliques have the so-called phase transitions when $f(n)$ is around the inverse function of the off-diagonal Ramsey number of $K_r$ versus a large clique $K_n$ for some $r\leq s$.
