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Almost spanning subgraphs of random graphs after adversarial edge removal

Böttcher, Julia and Kohayakawa, Yoshiharu and Taraz, Anusch (2013) Almost spanning subgraphs of random graphs after adversarial edge removal. Combinatorics, Probability and Computing, 22 (5). pp. 639-683. ISSN 0963-5483

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Identification Number: 10.1017/S0963548313000199

Abstract

Let Δ ≥ 2 be a fixed integer. We show that the random graph ${\mathcal{G}_{n,p}}$ with $p\gg (\log n/n)^{1/\Delta}$ is robust with respect to the containment of almost spanning bipartite graphs H with maximum degree Δ and sublinear bandwidth in the following sense: asymptotically almost surely, if an adversary deletes arbitrary edges from ${\mathcal{G}_{n,p}}$ in such a way that each vertex loses less than half of its neighbours, then the resulting graph still contains a copy of all such H.

Item Type: Article
Official URL: http://journals.cambridge.org/action/displayJourna...
Additional Information: © 2013 Cambridge University Press
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 12 Aug 2013 11:02
Last Modified: 17 Jun 2014 13:11
Projects: TA 309/2-1, EUBRANEX
Funders: German Research Foundation, Erasmus Mundus - External Cooperation Window
URI: http://eprints.lse.ac.uk/id/eprint/45822

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