1Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany 2Department of Mathematics and Computer Science, Emory University, Atlanta, USA 3Department of Discrete Mathematics, A. Mickiewicz University, Poznań, Poland
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 1023-1027
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Christian Reiher; Vojtěch Rödl; Andrzej Ruciński; Mathias Schacht; Bjarne Schülke; Christian Reiher; Vojtěch Rödl; Andrzej Ruciński; Mathias Schacht; Bjarne Schülke. Minimum pair-degee for tight Hamiltonian cycles in 4-uniform hypergraphs. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 1023-1027. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a103/
@article{AMUC_2019_88_3_a103,
author = {Christian Reiher and Vojt\v{e}ch R\"odl and Andrzej Ruci\'nski and Mathias Schacht and Bjarne Sch\"ulke and Christian Reiher and Vojt\v{e}ch R\"odl and Andrzej Ruci\'nski and Mathias Schacht and Bjarne Sch\"ulke},
title = { Minimum pair-degee for tight {Hamiltonian} cycles in 4-uniform hypergraphs},
journal = {Acta mathematica Universitatis Comenianae},
pages = {1023--1027},
year = {2019},
volume = {88},
number = {3},
url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a103/}
}
TY - JOUR
AU - Christian Reiher
AU - Vojtěch Rödl
AU - Andrzej Ruciński
AU - Mathias Schacht
AU - Bjarne Schülke
AU - Christian Reiher
AU - Vojtěch Rödl
AU - Andrzej Ruciński
AU - Mathias Schacht
AU - Bjarne Schülke
TI - Minimum pair-degee for tight Hamiltonian cycles in 4-uniform hypergraphs
JO - Acta mathematica Universitatis Comenianae
PY - 2019
SP - 1023
EP - 1027
VL - 88
IS - 3
UR - http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a103/
ID - AMUC_2019_88_3_a103
ER -
%0 Journal Article
%A Christian Reiher
%A Vojtěch Rödl
%A Andrzej Ruciński
%A Mathias Schacht
%A Bjarne Schülke
%A Christian Reiher
%A Vojtěch Rödl
%A Andrzej Ruciński
%A Mathias Schacht
%A Bjarne Schülke
%T Minimum pair-degee for tight Hamiltonian cycles in 4-uniform hypergraphs
%J Acta mathematica Universitatis Comenianae
%D 2019
%P 1023-1027
%V 88
%N 3
%U http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a103/
%F AMUC_2019_88_3_a103
We show that every 4-uniform hypergraph with n vertices and minimum pair-degree at least (5/9+o(1))n^2/2 contains a tight Hamiltonian cycle. This degree condition is asymptotically optimal. In the proof we use a variant of the absorbing method and ideas from the proof of the optimal minimum vertex degree condition for tight Hamiltonian cycles in 3-uniform hypergraphs that was obtained in a previous work by Reiher, Rödl, Ruciński, Schacht, and Szemerédi.
