eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-06-11
32:1
32:15
10.4230/LIPIcs.SoCG.2019.32
article
Cubic Planar Graphs That Cannot Be Drawn On Few Lines
Eppstein, David
1
Computer Science Department, University of California, Irvine, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol129-socg2019/LIPIcs.SoCG.2019.32/LIPIcs.SoCG.2019.32.pdf
graph drawing
universal point sets
collinearity