Shadow of Hypergraphs with Bounded Degree

Abstract

We study the size of the shadow of $k$-uniform hypergraphs with bounded degree. Lower bounds on the ratio of the size of the shadow and the size of the hypergraph are given as a function of the degree bound and $k$. We show that cliques are extremal for a long range of degree bounds, but not for every bound. We give a general, but not sharp lower bound on the shadow ratio and show, that sometimes we can get extremal hypergraphs by deleting disjoint maximal matchings from a clique.