Bounds on the Number of Edges of Edge-Minimal, Edge-Maximal and L-Hypertrees

Péter G.N. Szabó. "Bounds on the Number of Edges of Edge-Minimal, Edge-Maximal and L-Hypertrees." Discussiones Mathematicae Graph Theory 36.2 (2016): 259-278. <http://eudml.org/doc/277128>.

@article{PéterG2016,
abstract = {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 [...] .},
author = {Péter G.N. Szabó},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {hypertree; chain in hypergraph; edge-minimal hypertree; edge-maximal hypertree; 2-hypertree; Steiner system},
language = {eng},
number = {2},
pages = {259-278},
title = {Bounds on the Number of Edges of Edge-Minimal, Edge-Maximal and L-Hypertrees},
url = {http://eudml.org/doc/277128},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Péter G.N. Szabó
TI - Bounds on the Number of Edges of Edge-Minimal, Edge-Maximal and L-Hypertrees
JO - Discussiones Mathematicae Graph Theory
PY - 2016
VL - 36
IS - 2
SP - 259
EP - 278
AB - 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 [...] .
LA - eng
KW - hypertree; chain in hypergraph; edge-minimal hypertree; edge-maximal hypertree; 2-hypertree; Steiner system
UR - http://eudml.org/doc/277128
ER -