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Feedback Vertex Set on Hamiltonian Graphs

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Graph-Theoretic Concepts in Computer Science (WG 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12911))

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Abstract

We study the computational complexity of Feedback Vertex Set on subclasses of Hamiltonian graphs. In particular, we consider Hamiltonian graphs that are regular or are planar and regular. Moreover, we study the less known class of p-Hamiltonian-ordered graphs, which are graphs that admit for any p-tuple of vertices a Hamiltonian cycle visiting them in the order given by the tuple. We prove that Feedback Vertex Set remains \({\text {NP}}\)-hard in these restricted cases, even if a Hamiltonian cycle is additionally given as part of the input.

T. Fluschnik—Supported by DFG, project TORE (NI 369/18).

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Authors and Affiliations

  1. Faculty IV, Algorithmics and Computational Complexity, Technische Universität Berlin, Berlin, Germany

    Dario Cavallaro & Till Fluschnik

Authors
  1. Dario Cavallaro
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  2. Till Fluschnik
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Correspondence to Till Fluschnik .

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Editors and Affiliations

  1. University of Warsaw, Warsaw, Poland

    Łukasz Kowalik

  2. University of Warsaw, Warsaw, Poland

    Michał Pilipczuk

  3. Warsaw University of Technology, Warsaw, Poland

    Paweł Rzążewski

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Cavallaro, D., Fluschnik, T. (2021). Feedback Vertex Set on Hamiltonian Graphs. In: Kowalik, Ł., Pilipczuk, M., Rzążewski, P. (eds) Graph-Theoretic Concepts in Computer Science. WG 2021. Lecture Notes in Computer Science(), vol 12911. Springer, Cham. https://doi.org/10.1007/978-3-030-86838-3_16

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  • DOI: https://doi.org/10.1007/978-3-030-86838-3_16

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  • Print ISBN: 978-3-030-86837-6

  • Online ISBN: 978-3-030-86838-3

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