  A famous conjecture of Erd\H{o}s and S\'os states that every graph with
average degree more than $k - 1$ contains all trees with $k$ edges as
subgraphs. We prove that the Erd\H{o}s-S\'os conjecture holds approximately, if
the size of the embedded tree is linear in the size of the graph, and the
maximum degree of the tree is sublinear.
