On a problem of Erdős and Moser


A set A of vertices in an r-uniform hypergraph H is covered inH if there is some vertex u∉ A such that every edge of the form { u} ∪ B, B∈ A(r-1) is in H. Erdős and Moser (J Aust Math Soc 11:42–47, 1970) determined the minimum number of edges in a graph on n vertices such that every k-set is covered. We extend this result to r-uniform hypergraphs on sufficiently many vertices, and determine the extremal hypergraphs. We also address the problem for directed graphs.

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Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg