Loebl–Komlós–Sós Conjecture: Dense case

We prove a version of the Loebl–Komlós–Sós Conjecture for dense graphs. For each q>0q>0 there exists a number n0∈Nn0∈N such that for each n>n0n>n0 and k>qnk>qn the following holds: if G is a graph of order n   with at least n2 vertices of degree at least k  , then each tree of order k+1k+1 is a subgraph of G.