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Cubic Planar Graphs That Cannot Be Drawn On Few Lines

Author David Eppstein

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LIPIcs.SoCG.2019.32.pdf
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Author Details

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

Funding

  • Eppstein, David: Supported in part by NSF grants CCF-1618301 and CCF-1616248.

Cite As Get BibTex

David Eppstein. Cubic Planar Graphs That Cannot Be Drawn On Few Lines. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 32:1-32:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.SoCG.2019.32

Abstract

For every integer l, we construct a cubic 3-vertex-connected planar bipartite graph G with O(l^3) vertices such that there is no planar straight-line drawing of G whose vertices all lie on l lines. This strengthens previous results on graphs that cannot be drawn on few lines, which constructed significantly larger maximal planar graphs. We also find apex-trees and cubic bipartite series-parallel graphs that cannot be drawn on a bounded number of lines.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Human-centered computing → Graph drawings
Keywords
  • graph drawing
  • universal point sets
  • collinearity

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References

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