论文标题
图书图的数量
The Turán number of book graphs
论文作者
论文摘要
给定图形$ h $和一个正整数$ n，$ h $的$ h $ $ h $，$ n $ n，表示$ {\ rm ex}（n，h），$是简单的订单$ n $的最大尺寸，该订单$ n $不包含$ h $作为子Graph。带有$ p $页面的书，表示为$ b_p $，是由$ p $ triangles共享共同边缘的图表。 Bollobás和Erds在1975年开始了有关Turán数量图的研究。两个数字$ {\ rm ex}（p+2，b_p）$和$ {\ rm ex}（p+3，b_p）$由Qiao和Zhan确定。在本文中，我们确定数字$ {\ rm ex}（p+4，b_p），$ $ {\ rm ex}（p+5，b_p）$和$ {\ rm ex}（p+6，b_p），$，并表征数字$ $ {\ rm ex} $的相应的极端图$ n = p+2，\，p+3，\，p+4，\，p+5。$
Given a graph $H$ and a positive integer $n,$ the Turán number of $H$ for the order $n,$ denoted ${\rm ex}(n,H),$ is the maximum size of a simple graph of order $n$ not containing $H$ as a subgraph. The book with $p$ pages, denoted $B_p$, is the graph that consists of $p$ triangles sharing a common edge. Bollobás and Erdős initiated the research on the Turán number of book graphs in 1975. The two numbers ${\rm ex}(p+2,B_p)$ and ${\rm ex}(p+3,B_p)$ have been determined by Qiao and Zhan. In this paper we determine the numbers ${\rm ex}(p+4,B_p),$ ${\rm ex}(p+5,B_p)$ and ${\rm ex}(p+6,B_p),$ and characterize the corresponding extremal graphs for the numbers ${\rm ex}(n,B_p)$ with $n=p+2,\,p+3,\,p+4,\,p+5.$
