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Approximating Barnette’s Conjecture

Authors Michael A. Bekos , Michael Kaufmann , Maximilian Pfister

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LIPIcs.GD.2025.6.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorics
  • Mathematics of computing → Graph theory
Keywords
  • Barnette’s Conjecture
  • Subhamiltonicity
  • Book embeddings

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Abstract

A well-known conjecture, named after David W. Barnette, asserts that every 3-regular, 3-connected, bipartite, planar graph (for short, Barnette graph) is Hamiltonian. As another step towards addressing Barnette’s conjecture positively, we show that every n-vertex Barnette graph admits a subhamiltonian cycle containing 5n/6 edges, improving upon the previous bound of 2n/3. Equivalently, every Barnette graph admits a 2-page book embedding in which at least 5n/6 consecutive vertex pairs along the spine are connected by edges. As a byproduct, we present a simple proof for a known result that guarantees the existence of Hamiltonian cycles in a certain subclass of Barnette graphs.

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Michael A. Bekos, Michael Kaufmann, and Maximilian Pfister. Approximating Barnette’s Conjecture. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 6:1-6:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.GD.2025.6

Author Details

Michael A. Bekos
  • Department of Mathematics, University of Ioannina, Greece
Michael Kaufmann
  • Department of Computer Science, University of Tübingen, Germany
Maximilian Pfister
  • Department of Computer Science, University of Tübingen, Germany

Funding

  • Bekos, Michael A.: Supported by the HFRI grant 26320.
  • Pfister, Maximilian: Supported by the DFG grant SCHL 2331/1-1.

References

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