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 journalArticlepeer-review

3 Citations (Scopus)


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
Issue number2
Publication statusPublished - 2015 Mar 1
Externally publishedYes


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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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