This is the last of a series of four papers in which we prove the following relaxation of the Loebl-Komlós-Sós conjecture: For every α > 0 there exists a number k0 such that for every k > k0, every n-vertex graph G ...

This is the second of a series of four papers in which we prove the following relaxation of the Loebl-Komlós-Sós conjecture: For every α > 0 there exists a number k0 such that for every k > k0, every n-vertex graph ...

This is the third of a series of four papers in which we prove the following relaxation ofthe Loebl–Komlós–S ́os Conjecture: For everyα >0 there exists a numberk0such that foreveryk > k0everyn-vertex ...

In a series of four papers we prove the following relaxation of the Loebl–Koml ́os–S ́os Con-jecture: For everyα >0 there exists a numberk0such that for everyk > k0everyn-vertexgraphGwith at least (12+α)nvertices of degree ...

Loebl, Komlos and Sos conjectured that every n-vertex graph G with at least n/2 vertices of degree at least k contains each tree T of order k + 1 as a subgraph. We give a sketch of a proof of the approximate version of ...

Loebl, Komlos, and Sos conjectured that if at least half the vertices of a graph G have degree at least some k is an element of N, then every tree with at most k edges is a subgraph of G. We prove the conjecture for all ...