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A Graph Width Perspective on Partially Ordered Hamiltonian Paths and Cycles II: Vertex and Edge Deletion Numbers

Authors Jesse Beisegel , Katharina Klost , Kristin Knorr , Fabienne Ratajczak , Robert Scheffler

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LIPIcs.IPEC.2025.30.pdf
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ACM Subject Classification
  • Mathematics of computing → Paths and connectivity problems
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Hamiltonian path
  • Hamiltonian cycle
  • partial order
  • graph width parameter
  • parameterized complexity

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Abstract

We consider the problem of finding a Hamiltonian path or cycle with precedence constraints in the form of a partial order on the vertex set. We study the complexity for graph width parameters for which the ordinary problems Hamiltonian Path and Hamiltonian Cycle are in FPT. In particular, we focus on parameters that describe how many vertices and edges have to be deleted to become a member of a certain graph class. We show that the problems are W[1]-hard for such restricted cases as vertex distance to path and vertex distance to clique. We complement these results by showing that the problems can be solved in XP time for vertex distance to outerplanar and vertex distance to block. Furthermore, we present some FPT algorithms, e.g., for edge distance to block. Additionally, we prove para-NP-hardness when considered with the edge clique cover number.

Cite As Get BibTex

Jesse Beisegel, Katharina Klost, Kristin Knorr, Fabienne Ratajczak, and Robert Scheffler. A Graph Width Perspective on Partially Ordered Hamiltonian Paths and Cycles II: Vertex and Edge Deletion Numbers. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.IPEC.2025.30

Author Details

Jesse Beisegel
  • Institute of Mathematics, Brandenburg University of Technology, Cottbus, Germany
Katharina Klost
  • Institute of Computer Science, Freie Universität Berlin, Germany
Kristin Knorr
  • Institute of Computer Science, Freie Universität Berlin, Germany
Fabienne Ratajczak
  • Institute of Mathematics, Brandenburg University of Technology, Cottbus, Germany
Robert Scheffler
  • Institute of Mathematics, Brandenburg University of Technology, Cottbus, Germany

Funding

  • Ratajczak, Fabienne: The research was funded by the Federal Ministry for Digital and Transport Germany through the research project MoVeToLausitz (grant number 19FS2032C).

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