1Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 637-641
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Oliver Ebsen; Giulia Satiko Maesaka; Christian Reiher; Mathias Schacht; Bjarne Schülke; Oliver Ebsen; Giulia Satiko Maesaka; Christian Reiher; Mathias Schacht; Bjarne Schülke. Powers of Hamiltonian cycles in mu-inseparable graphs. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 637-641. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a43/
@article{AMUC_2019_88_3_a43,
author = {Oliver Ebsen and Giulia Satiko Maesaka and Christian Reiher and Mathias Schacht and Bjarne Sch\"ulke and Oliver Ebsen and Giulia Satiko Maesaka and Christian Reiher and Mathias Schacht and Bjarne Sch\"ulke},
title = { Powers of {Hamiltonian} cycles in mu-inseparable graphs},
journal = {Acta mathematica Universitatis Comenianae},
pages = {637--641},
year = {2019},
volume = {88},
number = {3},
url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a43/}
}
TY - JOUR
AU - Oliver Ebsen
AU - Giulia Satiko Maesaka
AU - Christian Reiher
AU - Mathias Schacht
AU - Bjarne Schülke
AU - Oliver Ebsen
AU - Giulia Satiko Maesaka
AU - Christian Reiher
AU - Mathias Schacht
AU - Bjarne Schülke
TI - Powers of Hamiltonian cycles in mu-inseparable graphs
JO - Acta mathematica Universitatis Comenianae
PY - 2019
SP - 637
EP - 641
VL - 88
IS - 3
UR - http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a43/
ID - AMUC_2019_88_3_a43
ER -
%0 Journal Article
%A Oliver Ebsen
%A Giulia Satiko Maesaka
%A Christian Reiher
%A Mathias Schacht
%A Bjarne Schülke
%A Oliver Ebsen
%A Giulia Satiko Maesaka
%A Christian Reiher
%A Mathias Schacht
%A Bjarne Schülke
%T Powers of Hamiltonian cycles in mu-inseparable graphs
%J Acta mathematica Universitatis Comenianae
%D 2019
%P 637-641
%V 88
%N 3
%U http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a43/
%F AMUC_2019_88_3_a43
We consider sufficient conditions for the existence of k-th powers of Hamiltonian cycles in n-vertex graphs G with minimum degree mu*n for arbitrarily small mu>0. About 20 years ago Komlós, Sárközy, and Szemerédi resolved the conjectures of Pósa and Seymour and obtained optimal minimum degree conditions for this problem by showing that mu=k/(k+1) suffices for large n. Consequently, for smaller values of mu the given graph G must satisfy additional assumptions. We show that inducing subgraphs of density d>0 on linear subsets of vertices and being inseparable, in the sense that every cut has density at least mu>0, are sufficient assumptions for this problem. This generalises a recent result of Staden and Treglown.
