An approximate version of the Loebl-Komlós-Sós conjecture

The Loebl–Komlós–Sós conjecture states that, given a graph G and a natural number k, if at least half the vertices of G have degree at least k, then any tree with at most k edges is a subgraph of G.We prove an approximate version of this conjecture for large graphs and k linear in |V(G)|.