Local resilience of spanning subgraphs in sparse random graphs
Allen, P.
, Böttcher, J., Ehrenmüller, J. & Taraz, A.
(2015-08-31 - 2015-09-04)
Local resilience of spanning subgraphs in sparse random graphs
[Paper]. European Conference on Combinatorics, Graph Theory and Applications, Bergen, Norway, NOR.
, Böttcher, J., Ehrenmüller, J. & Taraz, A.
(2015-08-31 - 2015-09-04)
Local resilience of spanning subgraphs in sparse random graphs
[Paper]. European Conference on Combinatorics, Graph Theory and Applications, Bergen, Norway, NOR.
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 n-vertex 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.