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 [...] 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 [...] .
@article{bwmeta1.element.doi-10_7151_dmgt_1855,
author = {P\'eter G.N. Szab\'o},
title = {Bounds on the Number of Edges of Edge-Minimal, Edge-Maximal and L-Hypertrees},
journal = {Discussiones Mathematicae Graph Theory},
volume = {36},
year = {2016},
pages = {259-278},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1855}
}
Péter G.N. Szabó. Bounds on the Number of Edges of Edge-Minimal, Edge-Maximal and L-Hypertrees. Discussiones Mathematicae Graph Theory, Tome 36 (2016) pp. 259-278. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1855/