论文标题
在最大$ f_5 $ - 无随机超图的无毛细管
On the Maximum $F_5$-free Subhypergraphs of a Random Hypergraph
论文作者
论文摘要
用$ f_5 $表示$ 3 $ - 均匀的超图，上面$ \ {1,2,3,4,5 \} $带有Hyperedges $ \ {123,124,345 \} $。 Balogh，Butterfield，Hu和Lenz证明，如果$ p> k \ log n / n $对于某些大常数$ k $，那么每个最大$ f_5 $ - f_5 $ - free subhypergraph $ g^3（n，p）$是较高的概率，并且表明，如果$ p_0 = 0.1 = 0.1 \ sqrt $ n $ n $ n $ n probiention a poc_ n} / n $ $ f_5 $ - $ g^3（n，p_0）$的$ free subhypergraph，不是三方。在本文中，我们将上限提高到最大可能的恒定因素。我们证明，如果$ p> c \ sqrt {\ log n} / n $对于某些大常数$ c $，则每个最大$ f_5 $ -f_5 $ -free subhypergraph $ g^3（n，p）$是三方，具有很高的可能性。
Denote by $F_5$ the $3$-uniform hypergraph on vertex set $\{1,2,3,4,5\}$ with hyperedges $\{123,124,345\}$. Balogh, Butterfield, Hu, and Lenz proved that if $p > K \log n / n$ for some large constant $K$, then every maximum $F_5$-free subhypergraph of $G^3(n,p)$ is tripartite with high probability, and showed that if $p_0 = 0.1\sqrt{\log n} / n$, then with high probability there exists a maximum $F_5$-free subhypergraph of $G^3(n,p_0)$ that is not tripartite. In this paper, we sharpen the upper bound to be best possible up to a constant factor. We prove that if $p > C \sqrt{\log n} / n $ for some large constant $C$, then every maximum $F_5$-free subhypergraph of $G^3(n, p)$ is tripartite with high probability.
