Geometric Biplane Graphs II: Graph Augmentation

Alfredo García, Ferran Hurtado, Matias Korman, Inês Matos, Maria Saumell, Rodrigo I. Silveira, Javier Tejel, Csaba D. Tóth

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We study biplane graphs drawn on a finite point set S in the plane in general position. This is the family of geometric graphs whose vertex set is S 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.

Original languageEnglish
Pages (from-to)427-452
Number of pages26
JournalGraphs and Combinatorics
Volume31
Issue number2
DOIs
Publication statusPublished - 2015 Mar 1

Keywords

  • Biplane graphs
  • Geometric graphs
  • Graph augmentation
  • k-connected graphs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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  • Cite this

    García, A., Hurtado, F., Korman, M., Matos, I., Saumell, M., Silveira, R. I., Tejel, J., & Tóth, C. D. (2015). Geometric Biplane Graphs II: Graph Augmentation. Graphs and Combinatorics, 31(2), 427-452. https://doi.org/10.1007/s00373-015-1547-0