Böttcher, Julia ORCID: 0000-0002-4104-3635, Parczyk, Olaf, Sgueglia, Amedeo and Skokan, Jozef
ORCID: 0000-0003-3996-7676
(2024)
The square of a Hamilton cycle in randomly perturbed graphs.
Random Structures and Algorithms, 65 (2).
342 - 386.
ISSN 1042-9832
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Text (The square of a Hamilton cycle in randomly in perturbed graphs)
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Abstract
We investigate the appearance of the square of a Hamilton cycle in the model of randomly perturbed graphs, which is, for a given α ∈ (0, 1), the union of any n-vertex graph with minimum degree αn and the binomial random graph G(n, p). This is known when α > 1/2 and we determine the exact perturbed threshold probability in all the remaining cases, i.e., for each α ≤ 1/2. We demonstrate that, as α ranges over the interval (0, 1), the threshold performs a countably infinite number of ‘jumps’. Our result has implications on the perturbed threshold for 2-universality, where we also fully address all open cases.
Item Type: | Article |
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Official URL: | https://onlinelibrary.wiley.com/journal/10982418 |
Additional Information: | © 2024 Wiley Periodicals LLC |
Divisions: | Mathematics |
Subjects: | Q Science > QA Mathematics |
Date Deposited: | 22 Jan 2024 10:21 |
Last Modified: | 15 Aug 2024 19:57 |
URI: | http://eprints.lse.ac.uk/id/eprint/121421 |
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