The Approximate Loebl--Komlós--Sós Conjecture I: The Sparse Decomposition
The Approximate Loebl--Komlós--Sós Conjecture I: The Sparse Decomposition
In a series of four papers we prove the following relaxation of the Loebl--Komlós--Sós conjecture: For every $\alpha>0$ there exists a number $k_0$ such that for every $k>k_0$, every $n$-vertex graph $G$ with at least $(\frac{1}{2}+\alpha)n$ vertices of degree at least $(1+\alpha)k$ contains each tree $T$ of order $k$ as …