Allen, Peter 
ORCID: 0000-0001-6555-3501, Böttcher, Julia ORCID: 0000-0002-4104-3635, Kohayakawa, Yoshiharu and Roberts, Barnaby
(2017)
Triangle-free subgraphs of random graphs.
Combinatorics, Probability and Computing, 27 (2).
pp. 141-161.
ISSN 0963-5483
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 |
| Divisions: |
Mathematics |
| Subjects: |
Q Science > QA Mathematics |
| Date Deposited: |
23 Jun 2016 09:58 |
| Last Modified: |
01 Oct 2024 03:44 |
| 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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