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.
@article{bwmeta1.element.doi-10_7151_dmgt_1947,
author = {Yi Lin and Liying Kang and Erfang Shan},
title = {Asymptotic Sharpness of Bounds on Hypertrees},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {789-795},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1947}
}
Yi Lin; Liying Kang; Erfang Shan. Asymptotic Sharpness of Bounds on Hypertrees. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 789-795. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1947/