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- ArticleJanuary 2023
- ArticleJanuary 2023
- articleMarch 2015
Geometric Biplane Graphs II: Graph Augmentation
- Alfredo García,
- Ferran Hurtado,
- Matias Korman,
- Inês Matos,
- Maria Saumell,
- Rodrigo I. Silveira,
- Javier Tejel,
- Csaba D. Tóth
Graphs and Combinatorics (GCOM), Volume 31, Issue 2Pages 427–452https://doi.org/10.1007/s00373-015-1547-0We study biplane graphs drawn on a finite point set $$S$$S in the plane in general position. This is the family of geometric graphs whose vertex set is $$S$$S and which can be decomposed into two plane graphs. We show that every sufficiently large point ...
- articleMarch 2015
Geometric Biplane Graphs I: Maximal Graphs
- Alfredo García,
- Ferran Hurtado,
- Matias Korman,
- Inês Matos,
- Maria Saumell,
- Rodrigo I. Silveira,
- Javier Tejel,
- Csaba D. Tóth
Graphs and Combinatorics (GCOM), Volume 31, Issue 2Pages 407–425https://doi.org/10.1007/s00373-015-1546-1We study biplane graphs drawn on a finite planar point set $$S$$S in general position. This is the family of geometric graphs whose vertex set is $$S$$S and can be decomposed into two plane graphs. We show that two maximal biplane graphs--in the sense ...
- articleMarch 2013
Computing a Hamiltonian Path of Minimum Euclidean Length Inside a Simple Polygon
Given an n-vertex convex polygon, we show that a shortest Hamiltonian path visiting all vertices without imposing any restriction on the starting and ending vertices of the path can be found in O(nlogn) time and ź(n) space. The time complexity increases ...
- articleFebruary 2011
Augmenting the Rigidity of a Graph in R2
Algorithmica (ALGR), Volume 59, Issue 2Pages 145–168Given a Laman graph G, i.e. a minimally rigid graph in R2, we provide a ź(n2) algorithm to augment G to a redundantly rigid graph, by adding a minimum number of edges. Moreover, we prove that this problem of augmenting is NP-hard for an arbitrary rigid ...
- articleFebruary 2011
Augmenting the Rigidity of a Graph in R 2
Algorithmica (ALGR), Volume 59, Issue 2Pages 145–168Given a Laman graph G, i.e. a minimally rigid graph in R 2, we provide a Θ(n 2) algorithm to augment G to a redundantly rigid graph, by adding a minimum number of edges. Moreover, we prove that this problem of augmenting is NP-hard for an arbitrary ...
- articleFebruary 2010
Augmenting the Connectivity of Outerplanar Graphs
Algorithmica (ALGR), Volume 56, Issue 2Pages 160–179We provide an optimal algorithm for the problem of augmenting an outerplanar graph G by adding a minimum number of edges in such a way that the augmented graph Gź is outerplanar and 2-connected. We also solve optimally the same problem when instead we ...