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The Approximate Loebl--Komlós--Sós Conjecture III: The Finer Structure of LKS Graphs

The Approximate Loebl--Komlós--Sós Conjecture III: The Finer Structure of LKS Graphs

This is the third of a series of four papers in which we prove the following relaxation of the Loebl-Komlos-Sos 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 $(\frac12+\alpha)n$ vertices of degree at least $(1+\alpha)k$ contains each …