Geometric Biplane Graphs II: Graph Augmentation

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 ar...

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Bibliographic Details
Published in:Graphs and combinatorics Vol. 31; no. 2; pp. 427 - 452
Main Authors: García, Alfredo, Hurtado, Ferran, Korman, Matias, Matos, Inês, Saumell, Maria, Silveira, Rodrigo I., Tejel, Javier, Tóth, Csaba D.
Format: Journal Article Publication
Language:English
Published: Tokyo Springer Japan 01.03.2015
Springer Nature B.V
Subjects:
30 Functions of a complex variable
30C Geometric function theory
Augmentation
Biplane graphs
Biplanes
Classificació AMS
Combinatorial analysis
Combinatorics
COMMON ANCESTORS
CONNECTIVITY
Engineering Design
Geometria
Geometria computacional
Geometric graphs
Geometric group theory
Geometry
Graph augmentation
Graph theory
Graphs
k-connected graphs
Matemàtiques i estadística
Mathematical analysis
Mathematics
Mathematics and Statistics
Original Paper
Planes
Texts
Wheels
Àrees temàtiques de la UPC
Biplane graphs
connected graphs
Geometric graphs
Graph augmentation
ISSN:0911-0119, 1435-5914
Online Access:Get full text
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Summary: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.
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ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-015-1547-0