We study feedback vertex sets (FVS) in tournaments, which are orientations of complete graphs. As our main result, we show that any tournament on n nodes has at most 1.5949n minimal FVS. This significantly improves the previously best upper bound of 1.6667n by Fomin et al. (STOC2016). Our new upper bound almost matches the best known lower bound of 21n/7 ≈ 1.5448n, due to Gaspers and Mnich (ESA 2010). Our proof is algorithmic, and shows that all minimal FVS of tournaments can be enumerated in time O(1.5949n).
|Series||Leibniz International Proceedings in Informatics (LIPIcs)|
- Exponential-time algorithms
- feedback vertex sets