Covering Complete Hypergraphs with Cuts of Minimum Total Size

A cut [X, V − X] in a hypergraph with vertex-set V is the set of all edges that meet both X and V − X. Let sr(n) denote the minimum total size of any cover of the edges of the complete r-uniform hypergraph on n vertices Kr n by cuts. We show that there is a number nr such that for every n > nr, sr(n) is uniquely achieved by a cover with ￿n−1 r−1 ￿ cuts [Xi, V − Xi] such that the Xi are pairwise disjoint sets of size at most

• Type: Journal
• Year: 2012
• Where: GC
• Authors: Sebastian M. Cioaba, André Kündgen
• Keywords: Applied Computing, GC 2012, Hypergraph, Vertex, Vertices