论文标题
禁止$ k_ {2，t} $三重系统中
Forbidding $K_{2,t}$ traces in triple systems
论文作者
论文摘要
令$ h $和$ f $为超图。我们说$ h $包含$ f $作为跟踪，如果存在某些set $ s \ subseteq v（h）$，以便$ h | _s：= \ {e \ cap s：e \ in E（h）\} $包含subhypergraph ishimypraph ishopermorphicsomorphic isomorphic to $ f $。在本文中，我们在$ 3 $均匀的超图中对边缘数量的上限给出了不包含$ k_ {2，t} $的trace的上限，当$ t $大。特别是，我们表明$ \ lim_ {t \ to \ infty} \ lim_ {n \ to \ infty} \ frac {\ mathrm {ex}（n，n，\ mathrm {tr} _3 _3（k_ {2，t}） \ frac {1} {6}。$ 此外，我们显示$ \ frac {1} {2} n^{3/2} + o（n^{3/2}）\ leq \ leq \ mathrm {ex}（n，n，\ mathrm {tr} _3（c_4）） o（n^{3/2}）$。
Let $H$ and $F$ be hypergraphs. We say $H$ contains $F$ as a trace if there exists some set $S \subseteq V(H)$ such that $H|_S:=\{E\cap S: E \in E(H)\}$ contains a subhypergraph isomorphic to $F$. In this paper we give an upper bound on the number of edges in a $3$-uniform hypergraph that does not contain $K_{2,t}$ as a trace when $t$ is large. In particular, we show that $ \lim_{t\to \infty}\lim_{n\to \infty} \frac{\mathrm{ex}(n, \mathrm{Tr}_3(K_{2,t}))}{t^{3/2}n^{3/2}} = \frac{1}{6}.$ Moreover, we show $\frac{1}{2} n^{3/2} + o(n^{3/2}) \leq \mathrm{ex}(n, \mathrm{Tr}_3(C_4)) \leq \frac{5}{6} n^{3/2} + o(n^{3/2})$.
