A proof of the Erdős-Faber-Lovász conjecture

Abstract

The Erdős-Faber-Lovász conjecture (posed in 1972) states that the chromatic index of any linear hypergraph on $n$ vertices is at most $n$. In this paper, we prove this conjecture for every large $n$. We also provide stability versions of this result, which confirm a prediction of Kahn.

arXiv comment47 pages, 3 figures. Final version, to appear in the Annals of Mathematics

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