### Abstract

We study combinatorial and algorithmic questions around minimal feedback vertex sets in tournament graphs.on the combinatorial side, we derive strong upper and lower bounds on the maximum number of minimal feedback vertex sets in an n-vertex tournament. We prove that every tournament on n vertices has at most 1.6740 n minimal feedback vertex sets and that there is an infinite family of tournaments, all having at least 1.5448 n minimal feedback vertex sets. This improves and extends the bounds of moon (1971).on the algorithmic side, we design the first polynomial space algorithm that enumerates the minimal feedback vertex sets of a tournament with polynomial delay. The combination of our results yields the fastest known algorithm for finding a minimum size feedback vertex set in a tournament.

Original language | English |
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Title of host publication | Algorithms - ESA 2010 |

Subtitle of host publication | 18th Annual European Symposium, Liverpool, UK, September 6-8, 2010. Proceedings, Part I |

Publisher | Springer |

Pages | 267-277 |

DOIs | |

Publication status | Published - 2010 |

Externally published | Yes |

### Publication series

Series | Lecture Notes in Computer Science |
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Volume | 6346 |

## Cite this

Gaspers, S., & Mnich, M. (2010). Feedback vertex sets in tournaments. In

*Algorithms - ESA 2010: 18th Annual European Symposium, Liverpool, UK, September 6-8, 2010. Proceedings, Part I*(pp. 267-277). Springer. Lecture Notes in Computer Science, Vol.. 6346 https://doi.org/10.1007/978-3-642-15775-2_23