اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe Tur{a}n number of book graphs
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Given a graph $H$ and a positive integer $n,$ the Tur{a}n 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. Bollob{a}s and ErdH{o}s initiated the research on the Tur{a}n 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 $n=p+2,,p+3,,p+4,,p+5.$
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For a graph $H$ and a $k$-chromatic graph $F,$ if the Turan graph $T_{k-1}(n)$ has the maximum number of copies of $H$ among all $n$-vertex $F$-free graphs (for $n$ large enough), then $H$ is called $F$-Turan-good, or $k$-Turan-good for short if $F$
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