Work

On the Biplanarity of Blowups

Year: 2024

Type: article

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.

Source: Journal of Graph Algorithms and Applications

DOI: 10.7155/jgaa.v28i2.2989

Author: David Eppstein

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Award: Collaborative Research: AF: Medium: Algorithms for Geometric Graphs

OpenAlex ID: W4403823171

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