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RSA
2011

Local resilience of almost spanning trees in random graphs

11 years 8 months ago
Local resilience of almost spanning trees in random graphs
We prove that for fixed integer D and positive reals α and γ, there exists a constant C0 such that for all p satisfying p(n) ≥ C0/n, the random graph G(n, p) asymptotically almost surely contains a copy of every tree with maximum degree at most D and at most (1 − α)n vertices, even after we delete a (1/2 − γ)-fraction of the edges incident to each vertex. The proof uses Szemer´edi’s regularity lemma for sparse graphs and a bipartite variant of the theorem of Friedman and Pippenger on embedding bounded degree trees into expanding graphs.
József Balogh, Béla Csaba, Wojciech
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where RSA
Authors József Balogh, Béla Csaba, Wojciech Samotij
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