We prove the following conjecture of S. Thomassé: for every (potentially infinite) digraph $D$ it is possible to iteratively reverse directed cycles in such a way that the dichromatic number of the final reorientation $D^{\ast }$ of $D$ is at most two and each edge is reversed only finitely many times. In addition, we guarantee that in every strong component of $D^{\ast }$ all the local edge-connectivities are finite and any edge is reversed at most twice.

中文翻译：

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通过无限次有向图中的循环反转减少二色数

我们证明S.Thomassé的以下猜想：对于每个（可能无限）的有向图 $d$ 可以以这样的方式迭代地反向定向循环，以使最终重定向的双色数 $d^{\ast }$ 的 $d$最多为两个，每个边仅反转有限次。此外，我们保证在$d^{\ast }$ 所有局部边的连接都是有限的，并且任何边最多反转两次。