A proof of the Erd\H{o}s-Faber-Lov\'asz 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. 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.

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