Loebl-Komlَs-Sَs Conjecture: dense case

We prove a version of the Loebl-Komlós-Sós Conjecture for large dense graphs. For any q > 0 there exists n 0 ∈ N such that for any n > n 0 holds: If G has median degree at least k, then any tree of order at most k + 1 is a subgraph of G.