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Local resilience of spanning subgraphs in sparse random graphs

Allen, Peter ORCID: 0000-0001-6555-3501, Böttcher, Julia ORCID: 0000-0002-4104-3635, Ehrenmüller, Julia and Taraz, Anusch (2015) Local resilience of spanning subgraphs in sparse random graphs. In: European Conference on Combinatorics, Graph Theory and Applications, 2015-08-31 - 2015-09-04, Bergen, Norway. (Submitted)

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Abstract

For each real γ>0γ>0 and integers Δ≥2Δ≥2 and k≥1k≥1, we prove that there exist constants β>0β>0 and C>0C>0 such that for all p≥C(log⁡n/n)1/Δp≥C(log⁡n/n)1/Δ the random graph G(n,p)G(n,p) asymptotically almost surely contains – even after an adversary deletes an arbitrary (1/k−γ1/k−γ)-fraction of the edges at every vertex – a copy of every n-vertex graph with maximum degree at most Δ, bandwidth at most βn and at least Cmax⁡{p−2,p−1log⁡n}Cmax⁡{p−2,p−1log⁡n} vertices not in triangles.

Item Type: Conference or Workshop Item (Paper)
Official URL: https://eurocomb2015.b.uib.no/
Additional Information: © 2015 The Authors
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 09 Dec 2015 11:38
Last Modified: 09 Nov 2021 00:08
URI: http://eprints.lse.ac.uk/id/eprint/64637

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