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Counting Triangulations of Fixed Cardinal Degrees (Poster Abstract)

Authors Erin Chambers , Tim Ophelders , Anna Schenfisch , Julia Sollberger

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Planar Triangulations
  • Degree Information
  • #P-Hardness

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Abstract

A fixed set of vertices in the plane may have multiple planar straight-line triangulations in which the degree of each vertex is the same. As such, the degree information does not completely determine the triangulation. We show that even if we know, for each vertex, the number of neighbors in each of the four cardinal directions, the triangulation is not completely determined. We show that counting such triangulations is #P-hard via a reduction from #3-regular bipartite planar vertex cover. pty

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Erin Chambers, Tim Ophelders, Anna Schenfisch, and Julia Sollberger. Counting Triangulations of Fixed Cardinal Degrees (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 46:1-46:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.GD.2025.46

Author Details

Erin Chambers
  • Department of Computer Science and Engineering, University of Notre Dame, IN, USA
Tim Ophelders
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
Anna Schenfisch
  • Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden
Julia Sollberger
  • Department of Mathematics, Vrije Universiteit Amsterdam, The Netherlands

Funding

  • Chambers, Erin: Research supported in part by the National Science Foundation under award CCF-2444309.
  • Ophelders, Tim: Partially supported by the Dutch Research Council (NWO) under project no. VI.Veni.212.260.
  • Schenfisch, Anna: Supported by the Dutch Research Council (NWO) under project no. P21-13.
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