# Cycles and Matchings in Randomly Perturbed Digraphs and Hypergraphs

@article{Krivelevich2016CyclesAM,
title={Cycles and Matchings in Randomly Perturbed Digraphs and Hypergraphs},
author={Michael Krivelevich and Matthew Kwan and Benny Sudakov},
journal={Combinatorics, Probability and Computing},
year={2016},
volume={25},
pages={909 - 927}
}
• Published 20 January 2015
• Mathematics
• Combinatorics, Probability and Computing
We give several results showing that different discrete structures typically gain certain spanning substructures (in particular, Hamilton cycles) after a modest random perturbation. First, we prove that adding linearly many random edges to a dense k-uniform hypergraph ensures the (asymptotically almost sure) existence of a perfect matching or a loose Hamilton cycle. The proof involves an interesting application of Szemerédi's Regularity Lemma, which might be independently useful. We next prove…
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