We prove that for integers $2 \leqslant \ell < k$ and a small constant $c$, if a $k$-uniform hypergraph with linear minimum codegree is randomly 'perturbed' by changing non-edges to edges independently at random with probability $p \geqslant O(n^{-(k-\ell)-c})$, then with high probability the resulting $k$-uniform hypergraph contains a Hamilton $\ell$-cycle. This complements a recent analogous result for Hamilton $1$-cycles due to Krivelevich, Kwan and Sudakov, and a comparable theorem in the graph case due to Bohman, Frieze and Martin.
@article{10_37236_7671,
author = {Andrew McDowell and Richard Mycroft},
title = {Hamilton \(\ell\)-cycles in randomly perturbed hypergraphs},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {4},
doi = {10.37236/7671},
zbl = {1402.05161},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7671/}
}
TY - JOUR
AU - Andrew McDowell
AU - Richard Mycroft
TI - Hamilton \(\ell\)-cycles in randomly perturbed hypergraphs
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/7671/
DO - 10.37236/7671
ID - 10_37236_7671
ER -
%0 Journal Article
%A Andrew McDowell
%A Richard Mycroft
%T Hamilton \(\ell\)-cycles in randomly perturbed hypergraphs
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/7671/
%R 10.37236/7671
%F 10_37236_7671
Andrew McDowell; Richard Mycroft. Hamilton \(\ell\)-cycles in randomly perturbed hypergraphs. The electronic journal of combinatorics, Tome 25 (2018) no. 4. doi: 10.37236/7671
