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The Approximate Loebl--Komlós--Sós Conjecture II: The Rough Structure of LKS Graphs

The Approximate Loebl--Komlós--Sós Conjecture II: The Rough Structure of LKS Graphs

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 $\alpha>0$ 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 …