The square of a Hamilton cycle in randomly perturbed graphs

Böttcher, Julia ORCID: 0000-0002-4104-3635, Parczyk, Olaf, Sgueglia, Amedeo and Skokan, Jozef ORCID: 0000-0003-3996-7676 (2021) The square of a Hamilton cycle in randomly perturbed graphs. In: Nešetřil, Jaroslav, Perarnau, Guillem, Rué, Juanjo and Serra, Oriol, (eds.) Extended Abstracts EuroComb 2021: European Conference on Combinatorics, Graph Theory and Applications. Research Perspectives CRM Barcelona. Birkhäuser (Firm), Cham, CH, 644 - 650. ISBN 9783030838225

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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. Our result has implications on the perturbed threshold for 2-universality, where we also fully address all open cases.

Item Type:	Book Section
Official URL:	https://link.springer.com/book/10.1007/978-3-030-8...
Additional Information:	© 2021 The Authors, under exclusive license to Springer Nature Switzerland AG.
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	23 Oct 2024 11:12
Last Modified:	11 Sep 2025 01:52
URI:	http://eprints.lse.ac.uk/id/eprint/125867

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