Embedding spanning trees in random graphs
Combinatorics
2010-08-19 v2
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^{\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)}.
Keywords
Cite
@article{arxiv.1007.2326,
title = {Embedding spanning trees in random graphs},
author = {Michael Krivelevich},
journal= {arXiv preprint arXiv:1007.2326},
year = {2010}
}
Comments
8 pages; minor updates, typos fixed