Скачать или смотреть Daniela Kühn - Proof of the Erdos-Faber-Lovasz Conjecture

The Erdős–Faber–Lovász conjecture (posed in 1972) states that the chromatic index of any
linear hypergraph on n vertices is at most n. (Here the chromatic index of a hypergraph
H is the smallest number of colours needed to colour the edges of H so that any two edges
that share a vertex have different colours.) Erdős considered this to be one of his three
most favorite combinatorial problems and offered $500 for the solution of the problem.
In a joint work with Dong-Yeap Kang, Tom Kelly, Abhishek Methuku and Deryk Osthus,
we prove this conjecture for every large n. We also provide “stability versions” of this
result, which confirm a prediction of Kahn.
In my talk, I will discuss some background, some of the ideas behind the proof, as well as
some related open problems.