Abstract
Given a graph F, a hypergraph is a Berge- F if it can be obtained by expanding each edge in F to a hyperedge containing it. A hypergraph H is Berge-F-saturated if H does not contain a subhypergraph that is a Berge-F, but for any edge e∈E(H¯), H+e does. The k-uniform saturation number of Berge-F is the minimum number of edges in a k-uniform Berge-F-saturated hypergraph on n vertices. For k=2 this definition coincides with the classical definition of saturation for graphs. In this paper we study the saturation numbers for Berge triangles, paths, cycles, stars and matchings in k-uniform hypergraphs.
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