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Triangle-free subgraphs of random graphs

Allen, Peter and Böttcher, Julia and Kohayakawa, Yoshiharu and Roberts, Barnaby (2017) Triangle-free subgraphs of random graphs. Combinatorics, Probability and Computing. ISSN 0963-5483

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Identification Number: 10.1017/S0963548317000219

Abstract

Recently there has been much interest in studying random graph analogues of well known classical results in extremal graph theory. Here we follow this trend and investigate the structure of triangle-free subgraphs of G(n, p) with high minimum degree. We prove that asymptotically almost surely each triangle-free spanning subgraph of G(n, p) with minimum degree at least ( 2 + o(1)lpn is O(p−1 n)-close to bipartite, and each spanning triangle-free subgraph of G(n, p) with minimum degree at least ( 1 + ε)pn is O(p−1 n)-close to r-partite for some r = r(ε). These are random graph analogues of a result by Andrásfai, Erdős and Sós [Discrete Math. 8 (1974), 205–218], and a result by Thomassen [Combinatorica 22 (2002), 591–596]. We also show that our results are best possible up to a constant factor.

Item Type: Article
Official URL: http://journals.cambridge.org/action/displayJourna...
Additional Information: © 2017 Cambridge University Press
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 23 Jun 2016 09:58
Last Modified: 19 Sep 2017 15:01
Projects: 013/03447-6, 2013/07699-0, 477203/2012-4, 310974/2013-5, 459335/2014-6, DMS 1102086, MaCLinC/USP
Funders: FAPESP, FAPESP, CNPq, CNPq, CNPq, NSF, NUMEC/USP
URI: http://eprints.lse.ac.uk/id/eprint/66985

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