On the Biplanarity of Blowups
Combinatorics
2024-10-29 v2
Abstract
The 2-blowup of a graph is obtained by replacing each vertex with two non-adjacent copies; a graph is biplanar if it is the union of two planar graphs. We disprove a conjecture of Gethner that 2-blowups of planar graphs are biplanar: iterated Kleetopes are counterexamples. Additionally, we construct biplanar drawings of 2-blowups of planar graphs whose duals have two-path induced path partitions, and drawings with split thickness two of 2-blowups of 3-chromatic planar graphs, and of graphs that can be decomposed into a Hamiltonian path and a dual Hamiltonian path.
Cite
@article{arxiv.2301.09246,
title = {On the Biplanarity of Blowups},
author = {David Eppstein},
journal= {arXiv preprint arXiv:2301.09246},
year = {2024}
}
Comments
15 pages, 8 figures. Appears in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023)