论文标题
Frankl-Kupavskii在边缘工会条件上的猜想的证明
A proof of Frankl-Kupavskii's conjecture on edge-union condition
论文作者
论文摘要
如果任何$ s $ s $ edges $ edges $ e_1，...，e_s \ in E（\ Mathcal {f}）$，$ s $ edges $ edges $ edges $ edges $ ed（\ mathcal {f}）$，$ | e_1 \ e_1 \ cup ... Frankl and Kupavskii（2020）提出了以下猜想：对于任何$ 3 $ -Graph $ \ Mathcal {f} $，带有$ n $ vertices，如果$ \ nathcal {f} $是$ u（s，2s+1），则是$ u（s，2s+1）$ （n-s-1）{s+1 \选择2}+{s+1 \选择3}，{2S+1 \选择3} \ right \}。$ $$在本文中，我们确认Frankl和Kupavskii的猜想。
A 3-graph $\mathcal{F}$ is \emph{$U(s, 2s+1)$} if for any $s$ edges $e_1,...,e_s\in E(\mathcal{F})$, $|e_1\cup...\cup e_s|\leq 2s+1$. Frankl and Kupavskii (2020) proposed the following conjecture: For any $3$-graph $\mathcal{F}$ with $n$ vertices, if $\mathcal{F}$ is $U(s, 2s+1)$, then $$e(\mathcal{F})\leq \max\left\{{n-1\choose 2}, (n-s-1){s+1\choose 2}+{s+1\choose 3}, {2s+1\choose 3}\right\}.$$ In this paper, we confirm Frankl and Kupavskii's conjecture.
