Cycle reversions and dichromatic number in tournaments

Paul Ellis, Daniel T. Soukup

Published 2017-08-08Version 1

We show that if $D$ is a tournament of arbitrary size then $D$ has finite strong components after reversing a locally finite sequence of cycles. In turn, we prove that any tournament can be covered by two acyclic sets after reversing a locally finite sequence of cycles. This provides a partial solution to a conjecture of S. Thomass\'e.