Geometric Biplane Graphs I: Maximal Graphs
Computational Geometry
2017-08-10 v1
Abstract
We study biplane graphs drawn on a finite planar point set in general position. This is the family of geometric graphs whose vertex set is and can be decomposed into two plane graphs. We show that two maximal biplane graphs---in the sense that no edge can be added while staying biplane---may differ in the number of edges, and we provide an efficient algorithm for adding edges to a biplane graph to make it maximal. We also study extremal properties of maximal biplane graphs such as the maximum number of edges and the largest maximum connectivity over -element point sets.
Cite
@article{arxiv.1702.01275,
title = {Geometric Biplane Graphs I: Maximal Graphs},
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:1702.01275},
year = {2017}
}