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 language | English |
|---|---|
| Pages (from-to) | 407-425 |
| Number of pages | 19 |
| Journal | Graphs and Combinatorics |
| Volume | 31 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 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