--------------------------------------------------------------------------- Joint Technion and University of Haifa Combinatorics Seminar --------------------------------------------------------------------------- The next meeting of the Combinatorics Seminar will take place on Wednesday, March 9 in *University of Haifa*. ** NOTICE THE CHANGE IN ROOM. ** Speaker: Michael Krivelevich (Tel Aviv University) Time: Wednesday, March 9, 13:10 Place: Science and Education Building, room #665, University of Haifa. Title: Embedding spanning trees in random graphs Abstract: We prove that if T is a tree on n vertices with maximum degree D and the edge probability p(n) satisfies: Np > c max{D*log n,n^{\epsilon}} for some positive \epsilon>0, then with high probability the random graph G(n,p) contains a copy of T. In particular, G(n,n^{-1+\epsilon}) whp contains a copy of any given bounded degree tree T on n vertices. The obtained bound on the edge probability is shown to be essentially tight for D=n^{\Theta(1)}. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Raphael Yuster <raphael.yuster@gmail.com>