论文标题
与奇数集团相交的Ramsey-Turán数字
Ramsey-Turán numbers for intersecting odd cliques
论文作者
论文摘要
给定图形$ h $和a函数$ f：\ mathbb {z}^+ \ longrightArrow \ mathbb {z}^+ $，ramsey-turán的$ h $和$ f $，用$ rt（n，h，h，f（n）$表示的$ n $ g a $ g as a $ a $ as a $ a a $ a a $ as a $ a a $ a a $ a a $ a a $ a y a $ a y a $ a a $ as a a $ a a $ a a $ a不包含一组$ f（n）$独立的顶点。让$ r $成为一个积极的整数。 1969年，Erdős和Sós证明了$ rt（n，k_ {2r+1}，o（n））= \ frac {n^2} {2} {2}（1- \ frac {1} {1} {r} {r} {r}）+o（n^2）$。令$ f_k（2r+1）$表示图形由$ k $的完整图的副本$ k_ {2r+1} $共享一个顶点。在本文中，我们表明$ rt（n，f_k（2r+1），o（n））= \ frac {n^2} {2} {2} {2}（1- \ frac {1} {1} {r} {r}）+O（n^2）$，与$ rt（n，k_ k_ k_ k_ {2r+1}} $（n）相同。
Given a graph $H$ and a function $f:\mathbb{Z}^+ \longrightarrow \mathbb{Z}^+ $, the Ramsey-Turán number of $H$ and $f$, denoted by $RT(n, H, f(n))$, is the maximum number of edges a graph $G$ on $n$ vertices can have, which does not contain $H$ as a subgraph and also does not contain a set of $f(n)$ independent vertices. Let $r$ be a positive integer. In 1969, Erdős and Sós proved that $RT(n,K_{2r+1},o(n))=\frac{n^2}{2}(1-\frac{1}{r})+o(n^2)$. Let $F_k(2r+1)$ denote the graph consisting of $k$ copies of complete graphs $K_{2r+1}$ sharing exactly one vertex. In this paper, we show that $RT(n,F_k(2r+1),o(n))=\frac{n^2}{2}(1-\frac{1}{r})+o(n^2)$, which is of the same magnitude with $RT(n, K_{2r+1}, o(n))$.
