  Loebl, Komlos, and Sos conjectured that if at least half of the vertices of a
graph G have degree at least some natural number k, then every tree with at
most k edges is a subgraph of G. Our main result is an approximate version of
this conjecture for large enough n=|V(G)|, assumed that n=O(k). Our result
implies an asymptotic bound for the Ramsey number of trees. We prove that
r(T_k,T_m)\leq k+m+o(k+m),as k+m tends to infinity.
