Year: 2026
Type: preprint
Abstract: 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 $n$-vertex finite simple loopless digraph with minimum out-degree at least $2k+g(k)$ contains $k$ disjoint directed cycles for all integers $k\ge K$ and $n\ge1$. In fact we obtain the explicit error term $g(k)=O(k^{3/4}\sqrt{\log k})$.
Source: arXiv (Cornell University)
Authors: Bang-Jensen, Jørgen, Wang, Guanghui, Wang, Yun
Institutions: Shandong University, University of Southern Denmark
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G493889870
OpenAlex ID: W7221069132