  Loebl, Komlos, and Sos conjectured that if at least half the vertices of a
graph G have degree at least some k, then every tree with at most k edges is a
subgraph of G. We prove the conjecture for all trees of diameter at most 5 and
for a class of caterpillars. Our result implies a bound on the Ramsey number
r(T,F) of trees T, F from the above classes.
