Resilience for tight Hamiltonicity

Allen, Peter ORCID: 0000-0001-6555-3501, Parczyk, Olaf and Pfenninger, Vincent (2024) Resilience for tight Hamiltonicity. Combinatorial Theory, 4 (1). ISSN 2766-1334

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Abstract

We prove that random hypergraphs are asymptotically almost surely resiliently Hamiltonian. Specifically, for any γ > 0 and k ≥ 3, we show that asymptotically almost surely, every subgraph of the binomial random k-uniform hypergraph G (k)(n, n γ−1) in which all (k − 1)-sets are contained in at least (1/2 + 2γ) pn edges has a tight Hamilton cycle. This is a cyclic ordering of the n vertices such that each consecutive k vertices forms an edge.

Item Type:	Article
Additional Information:	© 2024 The Author(s)
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	12 Jan 2024 14:27
Last Modified:	19 Nov 2024 00:54
URI:	http://eprints.lse.ac.uk/id/eprint/121362

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