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An asymptotic bound for the Bermond--Thomassen Conjecture
The Bermond--Thomassen Conjecture asserts that every digraph with minimum out-degree at least $2k-1$ contains $k$ disjoint directed cycles; it remains open in general. We asymptotically resolve it: there exist an absolute constant $K$ and a function $g(k)=o(k)$, independent of $n$, such that every $
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