We show that an n-vertex hypergraph with no r-regular subgraphs has at most 2n−1+r−2 edges. We conjecture that if n > r, then every n-vertex hypergraph with no r-regular subgraphs having the maximum number of edges contains a full star, that is, 2n−1 distinct edges containing a given vertex. We prove this conjecture for n ≥ 425. The condition that n > r cannot be weakened.
@article{bwmeta1.element.doi-10_7151_dmgt_1722,
author = {Jaehoon Kim and Alexandr V. Kostochka},
title = {Maximum Hypergraphs without Regular Subgraphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {34},
year = {2014},
pages = {151-166},
zbl = {1292.05201},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1722}
}
Jaehoon Kim; Alexandr V. Kostochka. Maximum Hypergraphs without Regular Subgraphs. Discussiones Mathematicae Graph Theory, Tome 34 (2014) pp. 151-166. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1722/
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