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A Polynomial Kernel for Face Cover on Non-Embedded Planar Graphs

Authors Thekla Hamm , Sukanya Pandey , Krisztina Szilágyi

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LIPIcs.STACS.2026.50.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Mathematics of computing → Graph algorithms
Keywords
  • Kernelization
  • Planar Graphs
  • SPQR-tree

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Abstract

Given a planar graph, a subset of its vertices called terminals, and k ∈ ℕ, the Face Cover Number problem asks whether the terminals lie on the boundaries of at most k faces of some embedding of the input graph. When a plane graph is given in the input, the problem is known to have a polynomial kernel [Valentin Garnero et al., 2017]. In this paper, we present the first polynomial kernel for Face Cover Number when the input is a planar graph (without a fixed embedding). Our approach overcomes the challenge of not having a predefined set of face boundaries by building a kernel bottom-up on an SPR-tree while preserving the essential properties of the face cover along the way.

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Thekla Hamm, Sukanya Pandey, and Krisztina Szilágyi. A Polynomial Kernel for Face Cover on Non-Embedded Planar Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 50:1-50:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.STACS.2026.50

Author Details

Thekla Hamm
  • TU Eindhoven, The Netherlands
Sukanya Pandey
  • RWTH Aachen University, Germany
Krisztina Szilágyi
  • Czech Technical University in Prague, Czech Republic

Funding

  • Hamm, Thekla: Supported by the Austrian Science Fund (J4651-N) during part of this work.
  • Szilágyi, Krisztina: Supported under the project Robotics and advanced industrial production (reg. no. CZ.02.01.01/00/22_008/0004590) and CTU Global Postdoc Fellowship Program.

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