Stability theorems for some Kruskal–Katona type results.

The classical Kruskal–Katona theorem gives a tight upper bound for the size of an r -uniform hypergraph H as a function of the size of its shadow. Its stability version was obtained by Keevash who proved that if the size of H is close to the maximum with respect to the size of its shadow, then 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. [ABSTRACT FROM AUTHOR]