Almost spanning subgraphs of random graphs after adversarial edge removal

Details Almost spanning subgraphs of random graphs after adversarial edge removal Almost spanning subgraphs of random graphs after adversarial edge removal

2010-03-03

arxiv.org/abs/1003.0890v1

Mathematics

Combinatorics

45 pages, 6 figures

Scientific paper

Let Delta>1 be a fixed integer. We show that the random graph G(n,p) with p>c*(log n/n)^{1/Delta} is robust with respect to the containment of almost spanning bipartite graphs H with maximum degree Delta and sublinear bandwidth in the following sense. If an adversary deletes arbitrary edges in G(n,p) such that each vertex loses less than half of its neighbours, then asymptotically almost surely the resulting graph still contains a copy of H.

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