论文标题
计数多个图表中的特拉问题
Counting multiple graphs in generalized Turán problems
论文作者
论文摘要
我们获得了图形$ H_1，\ dots，h_k $和$ f $。考虑$ n $顶点上的$ f $ f $ graph $ g $。 $ h_i $的副本数量最大的是多少？ $ k = 1 $引起了很多关注。 我们还考虑了彩色变体，其中$ g $的边缘上有$ k $颜色的颜色。 $ i $ $ h_i $ $ h_i $的副本数量最大的是多少？我们研究这种彩色变体的动机是最近的结果，指出$ r $ runiform berge- $ f $ hypergraphs的turán数量最多是上述数量，以$ k = 2 $，$ h_1 = k_r $和$ h_2 $和$ h_2 = k_2 $。 除了研究这些新问题外，我们还为广义的Turán问题以及Berge Hypergraphs获得了新的结果。
We are given graphs $H_1,\dots,H_k$ and $F$. Consider an $F$-free graph $G$ on $n$ vertices. What is the largest sum of the number of copies of $H_i$? The case $k=1$ has attracted a lot of attention. We also consider a colored variant, where the edges of $G$ are colored with $k$ colors. What is the largest sum of the number of copies of $H_i$ in color $i$? Our motivation to study this colored variant is a recent result stating that the Turán number of the $r$-uniform Berge-$F$ hypergraphs is at most the quantity defined above for $k=2$, $H_1=K_r$ and $H_2=K_2$. In addition to studying these new questions, we obtain new results for generalized Turán problems and also for Berge hypergraphs.
