论文标题
某些Kruskal-Katona类型结果的稳定定理
Stability theorems for some Kruskal-Katona type results
论文作者
论文摘要
经典的kruskal-katona定理给出了$ r $ rubiform HyperGraph $ \ Mathcal {H} $的大小，作为其阴影大小的函数。它的稳定版本是由Keevash获得的，他证明，如果$ \ Mathcal {H} $的大小接近最大值，则$ \ Mathcal {H} $在结构上接近完整的$ R $ rub-roniform-suorniform HyperGraph。我们证明了两类超图的稳定性结果相似，许多研究人员已经研究了许多研究人员：取消性超图和超图，而没有群集的扩大。
The classical Kruskal-Katona theorem gives a tight upper bound for the size of an $r$-uniform hypergraph $\mathcal{H}$ as a function of the size of its shadow. Its stability version was obtained by Keevash who proved that if the size of $\mathcal{H}$ is close to the maximum, then $\mathcal{H}$ is structurally close to a complete $r$-uniform hypergraph. We prove similar stability results for two classes of hypergraphs whose extremal properties have been investigated by many researchers: the cancellative hypergraphs and hypergraphs without expansion of cliques.
