# Almost spanning subgraphs of random graphs after adversarial edge removal

Böttcher, Julia, 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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## 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 http://journals.cambridge.org/action/displayJourna... © 2013 Cambridge University Press Q Science > QA Mathematics Departments > Mathematics http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx German Research Foundation, Erasmus Mundus - External Cooperation Window TA 309/2-1, EUBRANEX 12 Aug 2013 11:02 http://eprints.lse.ac.uk/45822/