Geometric Biplane Graphs II: Graph Augmentation
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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.
CitacióHurtado, F. [et al.]. Geometric Biplane Graphs II: Graph Augmentation. A: Mexican Conference on Discrete Mathematics and Computational Geometry. "Mexican Conference on Discrete Mathematics and Computational Geometry". Oaxaca: 2013, p. 223-234.