2021/09/16 by Jung, Attila
#05C35 #05C65 #05D05 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2109.08193
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.