Minimal asymmetric hypergraphs

Abstract

In this paper, we prove that for any k≥3, there exist infinitely many minimal asymmetric k-uniform hypergraphs. This is in a striking contrast to k=2, where it has been proved recently that there are exactly 18 minimal asymmetric graphs.We also determine, for every k≥1, the minimum size of an asymmetric k-uniform hypergraph.