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Parameterized Max Min Feedback Vertex Set

Authors Michael Lampis , Nikolaos Melissinos , Manolis Vasilakis

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Author Details

Michael Lampis
  • Université Paris-Dauphine, PSL University, CNRS, LAMSADE, 75016, Paris, France
Nikolaos Melissinos
  • Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Czech Republic
Manolis Vasilakis
  • Université Paris-Dauphine, PSL University, CNRS, LAMSADE, 75016, Paris, France


Work primarily conducted while Nikolaos Melissinos was affiliated with Université Paris-Dauphine.

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Michael Lampis, Nikolaos Melissinos, and Manolis Vasilakis. Parameterized Max Min Feedback Vertex Set. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 62:1-62:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


Given a graph G and an integer k, Max Min FVS asks whether there exists a minimal set of vertices of size at least k whose deletion destroys all cycles. We present several results that improve upon the state of the art of the parameterized complexity of this problem with respect to both structural and natural parameters. Using standard DP techniques, we first present an algorithm of time tw^O(tw) n^O(1), significantly generalizing a recent algorithm of Gaikwad et al. of time vc^O(vc) n^O(1), where tw, vc denote the input graph’s treewidth and vertex cover respectively. Subsequently, we show that both of these algorithms are essentially optimal, since a vc^o(vc) n^O(1) algorithm would refute the ETH. With respect to the natural parameter k, the aforementioned recent work by Gaikwad et al. claimed an FPT branching algorithm with complexity 10^k n^O(1). We point out that this algorithm is incorrect and present a branching algorithm of complexity 9.34^k n^O(1).

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • ETH
  • Feedback vertex set
  • Parameterized algorithms
  • Treewidth


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