5 research outputs found
Shadow of hypergraphs under a minimum degree condition
We prove a minimum degree version of the Kruskal--Katona theorem: given and a triple system on vertices with minimum degree at least
, we obtain asymptotically tight lower bounds for the size of its
shadow. Equivalently, for , we asymptotically determine the minimum
size of a graph on vertices, in which every vertex is contained in at least
triangles. This can be viewed as a variant of the
Rademacher--Tur\'an problem