Geodesic
Bounds on the Number of Edges of Edge-Minimal, Edge-Maximal and L-Hypertrees
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 2, pp. 259-278

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In their paper, Bounds on the number of edges in hypertrees, G.Y. Katona and P.G.N. Szabó introduced a new, natural definition of hypertrees in k-uniform hypergraphs and gave lower and upper bounds on the number of edges. They also defined edge-minimal, edge-maximal and l-hypertrees and proved an upper bound on the edge number of l-hypertrees. In the present paper, we verify the asymptotic sharpness of the nk-1 upper bound on the number of edges of k-uniform hypertrees given in the above mentioned paper. We also make an improvement on the upper bound of the edge number of 2-hypertrees and give a general extension construction with its consequences. We give lower and upper bounds on the maximal number of edges of k-uniform edge-minimal hypertrees and a lower bound on the number of edges of k-uniform edge-maximal hypertrees. In the former case, the sharp upper bound is conjectured to be asymptotically 1/k-1n2.
Keywords: hypertree, chain in hypergraph, edge-minimal hypertree, edge-maximal hypertree, 2-hypertree, Steiner system 
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     author = {Szab\'o, P\'eter G.N.},
     title = {Bounds on the {Number} of {Edges} of {Edge-Minimal,} {Edge-Maximal} and {L-Hypertrees}},
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Szabó, Péter G.N. Bounds on the Number of Edges of Edge-Minimal, Edge-Maximal and L-Hypertrees. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 2, pp. 259-278. http://geodesic.mathdoc.fr/item/DMGT_2016_36_2_a1/