论文标题
引起的Turán问题和超图的痕迹
Induced Turán problems and traces of hypergraphs
论文作者
论文摘要
令$ f $为图。我们说，如果可以将$ f $的顶点嵌入到$ h $（例如，$ v（f）\ subseteq v（h）$）并且存在$ f $ f $ $ f $ f $ f $ f $ f $ h $ h $ f（xy）$ f（xy）cap v $ f $ f $ f（xy）cap v $ f $ f（xy）cap v（f） \ {x，y \} $为$ f $的每个边缘$ xy $持有。换句话说，$ h $包含$ f $作为跟踪。 令$ ex_ {r}（n，b_ {ind} f）$表示$ r $ - 统一的超盖中的最大边数，而没有引起的berge $ f $。令$ ex（n，k_r，f）$表示$ n $顶点的$ f $ f $ fre图中的$ k_r $的最大数量。我们表明，这两个Turán型功能密切相关。
Let $F$ be a graph. We say that a hypergraph $H$ contains an induced Berge $F$ if the vertices of $F$ can be embedded to $H$ (e.g., $V(F)\subseteq V(H)$) and there exists an injective mapping $f$ from the edges of $F$ to the hyperedges of $H$ such that $f(xy) \cap V(F) = \{x,y\}$ holds for each edge $xy$ of $F$. In other words, $H$ contains $F$ as a trace. Let $ex_{r}(n,B_{ind} F)$ denote the maximum number of edges in an $r$-uniform hypergraph with no induced Berge $F$. Let $ex(n,K_r, F)$ denote the maximum number of $K_r$'s in an $F$-free graph on $n$ vertices. We show that these two Turán type functions are strongly related.
