Cubic planar graphs that cannot be drawn on few lines

Authors

  • David Eppstein University of California, Irvine

DOI:

https://doi.org/10.20382/v12i1a8

Abstract

For every integer $\ell$, we construct a cubic 3-vertex-connected planar bipartite graph $G$ with $O(\ell^3)$ vertices such that there is no planar straight-line drawing of $G$ whose vertices all lie on $\ell$ 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.

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Author Biography

David Eppstein, University of California, Irvine

Professor of Computer Science in the Donald Bren School of Information & Computer Sciences at the University of California, Irvine

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Published

2021-12-21

Issue

Vol. 12 No. 1 (2021)

Section

Articles

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