Geometric Biplane Graphs I: Maximal Graphs

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

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We study biplane graphs drawn on a finite planar point set S in general position. This is the family of geometric graphs whose vertex set is S 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 n-element point sets.

Original languageEnglish
Pages (from-to)407-425
Number of pages19
JournalGraphs and Combinatorics
Volume31
Issue number2
DOIs
Publication statusPublished - 2015 Mar 1

Keywords

  • Biplane graphs
  • Geometric graphs
  • Graph augmentation
  • K-Connected graphs
  • Maximal biplane 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 I: Maximal Graphs. Graphs and Combinatorics, 31(2), 407-425. https://doi.org/10.1007/s00373-015-1546-1