Hamilton ℓ-Cycles in Randomly Perturbed Hypergraphs

Research output: Contribution to journalArticlepeer-review

Colleges, School and Institutes

External organisations

  • King's College London

Abstract

We prove that for integers $2 \leq \ell < k$ 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 $p \geq O(n^{-(k-\ell)-c})$, 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.

Details

Original languageEnglish
Article numberP4.36
Number of pages30
JournalElectronic Journal of Combinatorics
Volume25
Issue number4
Publication statusPublished - 16 Nov 2018

Keywords

  • Hamilton cycles, Random Hypergraphs, Perturbing