The square of a Hamilton cycle in randomly in perturbed graphs

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 in perturbed graphs. Random Structures and Algorithms. ISSN 1042-9832

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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
Additional Information:	© 2024 Wiley Periodicals LLC
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	22 Jan 2024 10:21
Last Modified:	25 Apr 2024 11:12
URI:	http://eprints.lse.ac.uk/id/eprint/121421

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