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Stabbing Faces by a Convex Curve

Author David Eppstein

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LIPIcs.GD.2025.29.pdf
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ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • planar graphs
  • convex curves
  • stabbing
  • transversal

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Abstract

We prove that, for every plane graph G and every smooth convex curve C not on a single line, there exists a straight-line drawing of G for which every face is crossed by C.

Cite As Get BibTex

David Eppstein. Stabbing Faces by a Convex Curve. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 29:1-29:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.GD.2025.29

Author Details

David Eppstein
  • Computer Science Department, University of California, Irvine, CA, USA

Funding

  • Eppstein, David: Research supported in part by NSF grant CCF-2212129.

References

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