Geometric Biplane Graphs II: Graph Augmentation

Geometric Biplane Graphs II: Graph Augmentation

We study biplane graphs drawn on a nite 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 su ciently large point set admits a 5-connected biplane graph and that there are ar...

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Hauptverfasser: Hurtado Díaz, Fernando Alfredo, Garcia Olaverri, Alfredo Martin, Korman Cozzetti, Matías, Matos, Inés P, Saumell, Maria, Silveira, Rodrigo Ignacio, Tejel Altarriba, Francisco Javier, Tóth, Csaba D
Format: Text Resource
Sprache:eng
Schlagworte:
Geometria
Geometria computacional
Matemàtiques i estadística
Àrees temàtiques de la UPC
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Zusammenfassung:We study biplane graphs drawn on a nite 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 su ciently 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. Peer Reviewed