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

Discussiones Mathematicae Graph Theory (2016)

- Volume: 36, Issue: 2, page 259-278
- ISSN: 2083-5892

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topPéter 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 -

## References

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- [6] G.Y. Katona and P.G.N. Szab´o, Bounds on the number of edges in hypertrees. arXiv:1404.6430 [math.CO] (2014).
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