  Loebl, Koml\'os, and S\'os conjectured that any graph with at least half of
its vertices of degree at least k contains every tree with at most k edges. We
propose a version of this conjecture for skewed trees, i.e., we consider the
class of trees with at most k edges such that the sizes of the colour classes
of the trees have a given ratio. We show that our conjecture is asymptotically
correct for dense graphs. The proof relies on the regularity method. Our result
implies bounds on Ramsey number of several trees of given skew.
