# Asymptotic Sharpness of Bounds on Hypertrees

Yi Lin; Liying Kang; Erfang Shan

Discussiones Mathematicae Graph Theory (2017)

- Volume: 37, Issue: 3, page 789-795
- ISSN: 2083-5892

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topYi Lin, Liying Kang, and Erfang Shan. "Asymptotic Sharpness of Bounds on Hypertrees." Discussiones Mathematicae Graph Theory 37.3 (2017): 789-795. <http://eudml.org/doc/288341>.

@article{YiLin2017,

abstract = {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) $\left( \{\{n \cr \{k - 1\} \} \} \right)$ 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.},

author = {Yi Lin, Liying Kang, Erfang Shan},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {hypertree; semicycle in hypergraph; chain in hypergraph},

language = {eng},

number = {3},

pages = {789-795},

title = {Asymptotic Sharpness of Bounds on Hypertrees},

url = {http://eudml.org/doc/288341},

volume = {37},

year = {2017},

}

TY - JOUR

AU - Yi Lin

AU - Liying Kang

AU - Erfang Shan

TI - Asymptotic Sharpness of Bounds on Hypertrees

JO - Discussiones Mathematicae Graph Theory

PY - 2017

VL - 37

IS - 3

SP - 789

EP - 795

AB - 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) $\left( {{n \cr {k - 1} } } \right)$ 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.

LA - eng

KW - hypertree; semicycle in hypergraph; chain in hypergraph

UR - http://eudml.org/doc/288341

ER -

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