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Universality for bounded degree spanning trees in randomly perturbed graphs

Böttcher, Julia, Han, Jie, Kohayakawa, Yoshiharu, Montgomery, Richard, Parczyk, Olaf and Person, Yury (2019) Universality for bounded degree spanning trees in randomly perturbed graphs. Random Structures & Algorithms, 55 (4). pp. 854-864. ISSN 1042-9832

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Identification Number: 10.1002/rsa.20850

Abstract

We solve a problem of Krivelevich, Kwan and Sudakov concerning the threshold for the containment of all bounded degree spanning trees in the model of randomly perturbed dense graphs. More precisely, we show that, if we start with a dense graph G α on n vertices with δ(G α ) ≥ αn for α > 0 and we add to it the binomial random graph G(n,C/n), then with high probability the graph G α ∪G(n,C/n) contains copies of all spanning trees with maximum degree at most Δ simultaneously, where C depends only on α and Δ.

Item Type: Article
Additional Information: © 2019 The Authors
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 07 Feb 2019 10:36
Last Modified: 20 Oct 2020 05:32
URI: http://eprints.lse.ac.uk/id/eprint/100041

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