Feedback vertex sets in tournaments

Serge Gaspers, Matthias Mnich

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

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 languageEnglish
Title of host publicationAlgorithms - ESA 2010
Subtitle of host publication18th Annual European Symposium, Liverpool, UK, September 6-8, 2010. Proceedings, Part I
PublisherSpringer
Pages267-277
DOIs
Publication statusPublished - 2010
Externally publishedYes

Publication series

SeriesLecture Notes in Computer Science
Volume6346

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