Geodesic
Maximum Hypergraphs without Regular Subgraphs
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 1, pp. 151-166

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We show that an n-vertex hypergraph with no r-regular subgraphs has at most 2^n−1+r−2 edges. We conjecture that if n gt; r, then every n-vertex hypergraph with no r-regular subgraphs having the maximum number of edges contains a full star, that is, 2^n−1 distinct edges containing a given vertex. We prove this conjecture for n ≥ 425. The condition that n gt; r cannot be weakened.
Keywords: hypergraphs, set system, subgraph, regular graph 
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Kim, Jaehoon; Kostochka, Alexandr V. Maximum Hypergraphs without Regular Subgraphs. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 1, pp. 151-166. http://geodesic.mathdoc.fr/item/DMGT_2014_34_1_a12/