On a problem of Erdős and Moser
Abstract
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.
Publication Title
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Recommended Citation
Bollobás, B., & Scott, A. (2017). On a problem of Erdős and Moser. Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, 87 (2), 213-222. https://doi.org/10.1007/s12188-016-0162-1
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