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Almost Spanning Subgraphs of Random Graphs After Adversarial Edge Removal

Published online by Cambridge University Press:  08 August 2013

JULIA BÖTTCHER ,
YOSHIHARU KOHAYAKAWA  and
ANUSCH TARAZ
JULIA BÖTTCHER
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508–090 São Paulo, Brazil (e-mail: boettche@lse.ac.uk)
YOSHIHARU KOHAYAKAWA
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508–090 São Paulo, Brazil (e-mail: yoshi@ime.usp.br)
ANUSCH TARAZ
Affiliation:
Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, D–85747 Garching bei München, Germany (e-mail: taraz@ma.tum.de)
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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.

Keywords

Primary 05C35Secondary 05C8005C60

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 22 , Issue 5 , September 2013 , pp. 639 - 683
Copyright
Copyright © Cambridge University Press 2013 

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