论文标题
在$ k_m \ vee c_ {2k-1} $的turán数字上
On the Turán number of $K_m \vee C_{2k-1}$
论文作者
论文摘要
给定图形$ h $和一个正整数$ n $，订单$ n $的$ h $的turán数字，表示为$ ex（n，h）$，是一个简单的订单$ n $的最大大小，不包含$ h $作为子图。给定图表$ g $和$ h $，符号$ g \ vee h $表示$ g $和$ h $的关节。 $χ（g）$表示图形$ g $的色数。由于$χ（k_m \ vee c_ {2k-1}）= m+3 $，并且在e中有一个边缘$ e \（k_m \ vee c_ {2k-1} $ c_ {2k-1}）= \ lfloor \ frac {（m+1）n^2} {2（m+2）} \ rfloor $，用于足够大的$ n $。在本文中，我们证明$ 2（M+2）K-3（M+2）-1 $对于$ n $的大小足够大。
Given a graph $H$ and a positive integer $n$, the Turán number of $H$ for the order $n$, denoted $ex(n,H)$, is the maximum size of a simple graph of order $n$ not containing $H$ as a subgraph. Given graphs $G$ and $H$, the notation $G \vee H$ means the joint of $G$ and $H$. $χ(G)$ denotes the chromatic number of a graph $G$. Since $χ(K_m \vee C_{2k-1})=m+3$ and there is an edge $e\in E(K_m \vee C_{2k-1})$ such that $χ(K_m \vee C_{2k-1}-e)= m+2$, by the Simonovits theorem, $ex(n, K_m \vee C_{2k-1}) = \lfloor \frac{(m+1)n^2}{2(m+2)}\rfloor$ for sufficiently large $n$. In this paper, we prove that $2(m+2)k-3(m+2)-1$ is large enough for $n$.
