Geometric Biplane Graphs II: Graph Augmentation
Computational Geometry
2017-08-10 v1
Abstract
We study biplane graphs drawn on a finite point set in the plane in general position. This is the family of geometric graphs whose vertex set is and which can be decomposed into two plane graphs. We show that every sufficiently large point set admits a 5-connected biplane graph and that there are arbitrarily large point sets that do not admit any 6-connected biplane graph. Furthermore, we show that every plane graph (other than a wheel or a fan) can be augmented into a 4-connected biplane graph. However, there are arbitrarily large plane graphs that cannot be augmented to a 5-connected biplane graph by adding pairwise noncrossing edges.
Cite
@article{arxiv.1702.01277,
title = {Geometric Biplane Graphs II: Graph Augmentation},
author = {Alfredo García and Ferran Hurtado and Matias Korman and Inês Matos and Maria Saumell and Rodrigo I. Silveira and Javier Tejel and Csaba D. Tóth},
journal= {arXiv preprint arXiv:1702.01277},
year = {2017}
}