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 1.6740n minimal feedback vertex sets and that there is an infinite family of tournaments, all having at least 1.5448n 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.
Part of this research has been supported by the Netherlands Organisation for Scientific Research (NWO), grant 639.033.403.
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Gaspers, S., Mnich, M. (2010). Feedback Vertex Sets in Tournaments. In: de Berg, M., Meyer, U. (eds) Algorithms – ESA 2010. ESA 2010. Lecture Notes in Computer Science, vol 6346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15775-2_23
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DOI: https://doi.org/10.1007/978-3-642-15775-2_23
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