Saturation for the $3$-uniform loose $3$-cycle

Abstract

Let F and H be k-uniform hypergraphs. We say H is F -saturated if H does not contain a subgraph isomorphic to F , but H + e does for any hyperedge e ∈ E(H). The saturation number of F , denoted sat k (n, F ), is the minimum number of edges in a F -saturated k-uniform hypergraph H on n vertices. Let C(3) 3 denote the 3-uniform loose cycle on 3 edges. In this work, we prove that3 ) ≤This is the first non-trivial result on the saturation number for a fixed short hypergraph cycle.