2026-07-28T01:14:54Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:6923 2024-03-06T10:38:49Z ddc:004 open_access

Improved Bounds for Minimal Feedback Vertex Sets in Tournaments Mnich, Matthias Teutrine, Eva-Lotta exponential-time algorithms feedback vertex sets tournaments 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 1.5949^n minimal FVS. This significantly improves the previously best upper bound of 1.6667^n by Fomin et al. (STOC 2016). Our new upper bound almost matches the best known lower bound of 21^{n/7} approx 1.5448^n, 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(1.5949^n). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Matthias Mnich and Eva-Lotta Teutrine 2017 Is Part Of LIPIcs, Volume 63, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.IPEC.2016.24 urn:nbn:de:0030-drops-69236 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2016.24 eng https://creativecommons.org/licenses/by/3.0/legalcode