English

Cycle reversions and dichromatic number in tournaments

Combinatorics 2017-08-09 v1 Logic

Abstract

We show that if DD is a tournament of arbitrary size then DD 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.

Keywords

Cite

@article{arxiv.1708.02441,
  title  = {Cycle reversions and dichromatic number in tournaments},
  author = {Paul Ellis and Daniel T. Soukup},
  journal= {arXiv preprint arXiv:1708.02441},
  year   = {2017}
}

Comments

23 pages, first public version. Comments are very welcome