Embedding spanning trees in random graphs

Details Embedding spanning trees in random graphs Embedding spanning trees in random graphs

2010-07-14

arxiv.org/abs/1007.2326v2

Mathematics

Combinatorics

8 pages; minor updates, typos fixed

Scientific paper

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^{\epsilon}} for some constant
\epsilon>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^{\Theta(1)}.

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