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arXiv · 1007.2326

Embedding spanning trees in random graphs

Michael Krivelevich
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Abstract

We prove that if T is a tree on n vertices wih maximum degree D and the edge probability p(n) satisfies: np>c*max{D*logn,n^ε} for some constant ε>0, then with high probability the random graph G(n,p) contains a copy of T. The obtained bound on the edge probability is shown to be essentially tight for D=n^{Θ(1)}.

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Michael Krivelevich. 2010-08-18. Embedding spanning trees in random graphs. https://arxiv.org/abs/1007.2326

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