Reducing the dichromatic number via cycle reversions in infinite digraphs. (December 2020) - Ellis, Paul; Joó, Attila; Soukup, Dániel T.
Abstract: 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 ∗ 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 ∗ all the local edge-connectivities are finite and any edge is reversed at most twice.