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Improved Bounds for Minimal Feedback Vertex Sets in Tournaments

Authors Matthias Mnich, Eva-Lotta Teutrine



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Matthias Mnich
Eva-Lotta Teutrine

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Matthias Mnich and Eva-Lotta Teutrine. Improved Bounds for Minimal Feedback Vertex Sets in Tournaments. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 24:1-24:10, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.IPEC.2016.24

Abstract

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).
Keywords
  • exponential-time algorithms
  • feedback vertex sets
  • tournaments

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