Allen, Peter and Böttcher, Julia and Ehrenmüller, Julia and Taraz, Anusch
(2015)
Local resilience of spanning subgraphs in sparse random graphs.
In: European Conference on Combinatorics, Graph Theory and Applications, 31 August  04 September 2015, Bergen, Norway.
(Unpublished)
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(logn/n)1/Δp≥C(logn/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 nvertex graph with maximum degree at most Δ, bandwidth at most βn and at least Cmax{p−2,p−1logn}Cmax{p−2,p−1logn} vertices not in triangles.
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