论文标题
将家庭与第三名相交
Intersecting families with covering number three
论文作者
论文摘要
我们考虑$ n $ VERTICES上的$ K $ -Graphs，即$ \ Mathcal {f} \ subset \ binom {[n]} {k} $。如果$ f \ cap f'\ neq \ emptyset $ for a pherseet f，in \ mathcal {f} $，a $ k $ -graph $ \ mathcal {f} $如果$ f \ cap f'\ neq \ emptyset $称为相交。在本文中，我们证明，对于$ k \ geq 7 $，$ n \ geq 2k $，任何相交的$ k $ -graph $ \ mathcal {f} $与覆盖号码至少三个，满足$ | \ Mathcal {f} | \ leq \ binom {n-1} {k-1} - \ binom {n-k} {k-1} - \ binom {n-k-1} {n-k-1} {k-1} {k-1}+\ binom {n-2k} {k-1} {k-1} {k-1}+\ binom {n-k-binom {n-k-k-2} \ cite {f80}受指数约束的约束$ n> n_0（k）$。
We consider $k$-graphs on $n$ vertices, that is, $\mathcal{F}\subset \binom{[n]}{k}$. A $k$-graph $\mathcal{F}$ is called intersecting if $F\cap F'\neq \emptyset$ for all $F,F'\in \mathcal{F}$. In the present paper we prove that for $k\geq 7$, $n\geq 2k$, any intersecting $k$-graph $\mathcal{F}$ with covering number at least three, satisfies $|\mathcal{F}|\leq \binom{n-1}{k-1}-\binom{n-k}{k-1}-\binom{n-k-1}{k-1}+\binom{n-2k}{k-1}+\binom{n-k-2}{k-3}+3$, the best possible upper bound which was proved in \cite{F80} subject to exponential constraints $n>n_0(k)$.
