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Vertex Cover and Feedback Vertex Set Above and Below Structural Guarantees

Authors Leon Kellerhals , Tomohiro Koana , Pascal Kunz

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Leon Kellerhals
  • Faculty IV, Institute of Software Engineering and Theoretical Computer Science, Algorithmics and Computational Complexity, Technische Universität Berlin, Germany
Tomohiro Koana
  • Faculty IV, Institute of Software Engineering and Theoretical Computer Science, Algorithmics and Computational Complexity, Technische Universität Berlin, Germany
Pascal Kunz
  • Faculty IV, Institute of Software Engineering and Theoretical Computer Science, Algorithmics and Computational Complexity, Technische Universität Berlin, Germany


This work was initiated at the research retreat of the Algorithmics and Computational Complexity group, TU Berlin, in 2021.

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Leon Kellerhals, Tomohiro Koana, and Pascal Kunz. Vertex Cover and Feedback Vertex Set Above and Below Structural Guarantees. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 19:1-19:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Vertex Cover parameterized by the solution size k is the quintessential fixed-parameter tractable problem. FPT algorithms are most interesting when the parameter is small. Several lower bounds on k are well-known, such as the maximum size of a matching. This has led to a line of research on parameterizations of Vertex Cover by the difference of the solution size k and a lower bound. The most prominent cases for such lower bounds for which the problem is FPT are the matching number or the optimal fractional LP solution. We investigate parameterizations by the difference between k and other graph parameters including the feedback vertex number, the degeneracy, cluster deletion number, and treewidth with the goal of finding the border of fixed-parameter tractability for said difference parameterizations. We also consider similar parameterizations of the Feedback Vertex Set problem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • parameterized complexity
  • vertex cover
  • feedback vertex set
  • above guarantee parameterization


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