On a problem of Erdős and Moser
نویسندگان
چکیده
A set A of vertices in an r-uniform hypergraph H is covered in H if there is some vertex u 6∈ A such that every edge of form {u} ∪ B, B ∈ A(r−1) is in H. Erdős and Moser (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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