Cycle reversions and dichromatic number in tournaments
2019
Abstract We show that if D is a tournament of arbitrary size then D can be made to have only finite strong components after reversing a locally finite sequence of cycles. In turn, we prove that the vertex set of any tournament can be covered by two acyclic induced subgraphs after reversing a locally finite sequence of cycles. This provides a partial solution to a conjecture of S. Thomasse.
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