论文标题
关于超图形痕迹的Turán编号的注释
A note on the Turán number for the traces of hypergraphs
论文作者
论文摘要
令$ \ MATHCAL {H} $为$ R $ - 均匀的超图，$ f $为图。我们说$ \ Mathcal {h} $将$ f $包含作为跟踪，如果某些设置$ s \ subseteq v（\ MathCal {h}）$，以至于$ \ nathcal {h} | _ {s} | _ {s}：= \ = \ {e \ cap s：e \ in（e e（e e e \ in e s s s s sel） $ F. $ LET $ ex_r（n，tr（f））$表示$ n $ -vertex $ r $ r $ r $ rustraph $ \ mathcal {h} $的最大边数，该边缘不包含$ f $作为跟踪。在本文中，当$ f $是星星并给出一些最佳案例时，我们改善了$ ex_r（n，tr（f））$的下限。当$ \ Mathcal {h} $为$ 3 $ - 统一，而$ f $为$ k_ {2，t} $时，我们还改善了上限的上限。
Let $\mathcal{H}$ be an $r$-uniform hypergraph and $F$ be a graph. We say $\mathcal{H}$ contains $F$ as a trace if there exists some set $S\subseteq V(\mathcal{H})$ such that $\mathcal{H}|_{S}:=\{E\cap S: E\in E(\mathcal{H})\}$ contains a subgraph isomorphic to $F.$ Let $ex_r(n,Tr(F))$ denote the maximum number of edges of an $n$-vertex $r$-uniform hypergraph $\mathcal{H}$ which does not contain $F$ as a trace. In this paper, we improve the lower bounds of $ex_r(n,Tr(F))$ when $F$ is a star, and give some optimal cases. We also improve the upper bound for the case when $\mathcal{H}$ is $3$-uniform and $F$ is $K_{2,t}$ when $t$ is small.
