2017/10/10 by English, Sean, Graber, Nathan, Kirkpatrick, Pamela +2
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1710.03735
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 subgraph 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.