Cycles and matchings in randomly perturbed digraphs and hypergraphs

Krivelevich M, Kwan MA, Sudakov B. 2015. Cycles and matchings in randomly perturbed digraphs and hypergraphs. Electronic Notes in Discrete Mathematics. 49, 181–187.


Journal Article | Published | English

Scopus indexed
Author
Krivelevich, Michael; Kwan, Matthew AlanIST Austria; Sudakov, Benny
Abstract
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 that digraphs with certain strong expansion properties are pancyclic, and use this to show that adding a linear number of random edges typically makes a dense digraph pancyclic. Finally, we prove that perturbing a certain (minimum-degree-dependent) number of random edges in a tournament typically ensures the existence of multiple edge-disjoint Hamilton cycles. All our results are tight.
Publishing Year
Date Published
2015-11-01
Journal Title
Electronic Notes in Discrete Mathematics
Volume
49
Page
181-187
ISSN
IST-REx-ID

Cite this

Krivelevich M, Kwan MA, Sudakov B. Cycles and matchings in randomly perturbed digraphs and hypergraphs. Electronic Notes in Discrete Mathematics. 2015;49:181-187. doi:10.1016/j.endm.2015.06.027
Krivelevich, M., Kwan, M. A., & Sudakov, B. (2015). Cycles and matchings in randomly perturbed digraphs and hypergraphs. Electronic Notes in Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.endm.2015.06.027
Krivelevich, Michael, Matthew Alan Kwan, and Benny Sudakov. “Cycles and Matchings in Randomly Perturbed Digraphs and Hypergraphs.” Electronic Notes in Discrete Mathematics. Elsevier, 2015. https://doi.org/10.1016/j.endm.2015.06.027.
M. Krivelevich, M. A. Kwan, and B. Sudakov, “Cycles and matchings in randomly perturbed digraphs and hypergraphs,” Electronic Notes in Discrete Mathematics, vol. 49. Elsevier, pp. 181–187, 2015.
Krivelevich M, Kwan MA, Sudakov B. 2015. Cycles and matchings in randomly perturbed digraphs and hypergraphs. Electronic Notes in Discrete Mathematics. 49, 181–187.
Krivelevich, Michael, et al. “Cycles and Matchings in Randomly Perturbed Digraphs and Hypergraphs.” Electronic Notes in Discrete Mathematics, vol. 49, Elsevier, 2015, pp. 181–87, doi:10.1016/j.endm.2015.06.027.
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