Geodesic
Asymptotic Sharpness of Bounds on Hypertrees
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 789-795

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The hypertree can be defined in many different ways. Katona and Szabó introduced a new, natural definition of hypertrees in uniform hypergraphs and investigated bounds on the number of edges of the hypertrees. They showed that a k-uniform hypertree on n vertices has at most nk−1 edges and they conjectured that the upper bound is asymptotically sharp. Recently, Szabó verified that the conjecture holds by recursively constructing an infinite sequence of k-uniform hypertrees and making complicated analyses for it. In this note we give a short proof of the conjecture by directly constructing a sequence of k-uniform k-hypertrees.
Keywords: hypertree, semicycle in hypergraph, chain in hypergraph 
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Lin, Yi; Kang, Liying; Shan, Erfang. Asymptotic Sharpness of Bounds on Hypertrees. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 789-795. http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a19/