The Loebl-Komlos-Sos conjecture asserts that any graph of order n
which has at least half of its vertices of degrees at least k contains
any tree with k edges as a subgraph. In the talk, I shall sketch a
proof of this conjecture in the case when k is linear in n. The proof
uses the Regularity lemma and combines tools developed by Piguet and
Stein and by Zhao. This is joint work with Diana Piguet.