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A proof of the Erdős-Faber-Lovász conjecture

Published 12 Jan 2021 in math.CO | (2101.04698v3)

Abstract: The Erd\H{o}s-Faber-Lov\'{a}sz 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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