论文标题
在具有固定匹配和集团数字的超图中的最大边缘数量上
On the Maximum Number of Edges in Hypergraphs with Fixed Matching and Clique Number
论文作者
论文摘要
对于$ k $ -graph $ \ Mathcal {f} \ subset \ binom {[n]} {k} $，定义为$ \ nathcal {f} $的clique数字是$ \ \ binom {q} $ {q} $ {q subset的$ q $ q of $ q $ q $的最大大小。在本文中，我们确定了$ k $ - 图中的最大边数，$ k $ - $ [n] $，最多匹配的$ s $和clique号码至少$ q $，对于$ n \ geq 8k^2s $，以及$ q \ q \ geq（s+1）k-l $，$ n \ n \ leq（s+1）k+s+s+s/（s+1）k+s/（3k）。 $ q =（s+1）k-2 $和$ k = 2 $的两种特殊情况已完全解决。
For a $k$-graph $\mathcal{F}\subset \binom{[n]}{k}$, the clique number of $\mathcal{F}$ is defined to be the maximum size of a subset $Q$ of $[n]$ with $\binom{Q}{k}\subset \mathcal{F}$. In the present paper, we determine the maximum number of edges in a $k$-graph on $[n]$ with matching number at most $s$ and clique number at least $q$ for $n\geq 8k^2s$ and for $q \geq (s+1)k-l$, $n\leq (s+1)k+s/(3k)-l$. Two special cases that $q=(s+1)k-2$ and $k=2$ are solved completely.
