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- Alfredo García Olaverri, Marc Noy, Javier Tejel
- Comput. Geom.
- 2000

- Manuel Abellanas, Alfredo García Olaverri, Ferran Hurtado, Javier Tejel, Jorge Urrutia
- Comput. Geom.
- 2008

Let G be a connected plane geometric graph with n vertices. In this paper, we study bounds on the number of edges required to be added to G to obtain 2-vertex or 2-edge connected plane geometric graphs. In particular, we show that for G to become 2-edge connected, 2n 3 additional edges are required in some cases and that 6n 7 additional edges are always… (More)

- Alfredo García Olaverri, M. Carmen Hernando, Ferran Hurtado, Marc Noy, Javier Tejel
- Journal of Graph Theory
- 1997

- Manuel Abellanas, Sergey Bereg, Ferran Hurtado, Alfredo García Olaverri, David Rappaport, Javier Tejel
- Comput. Geom.
- 2006

We consider combinatorial and computational issues that are related to the problem of moving coins from one configuration to another. Coins are defined as non-overlapping discs, and moves are defined as collision free translations, all in the Euclidean plane. We obtain combinatorial bounds on the number of moves that are necessary and/or sufficient to move… (More)

- O. Aichholzer, A. Garćıa, F. Hurtado, J. Tejel
- 2011

Two non-crossing geometric graphs on the same set of points are compatible if their union is also non-crossing. In this paper, we prove that every graph G that has an outerplanar embedding admits a non-crossing perfect matching compatible with G. Moreover, for non-crossing geometric trees and simple polygons, we study bounds on the minimum number of edges… (More)

- Alfredo García Olaverri, Javier Tejel
- Algorithmica
- 2009

Given 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 rigid graph G in R 2.

- Alfredo García Olaverri, Ferran Hurtado, Clemens Huemer, Javier Tejel, Pavel Valtr
- Comput. Geom.
- 2009

- Alfredo García Olaverri, Ferran Hurtado, Marc Noy, Javier Tejel
- Algorithmica
- 2008

We 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 G′ is outerplanar and 2-connected. We also solve optimally the same problem when instead we require G′ to be 2-edge-connected.

- Alfredo García Olaverri, Javier Tejel
- Inf. Process. Lett.
- 1996

- Javier Cano, Alfredo García Olaverri, Ferran Hurtado, Toshinori Sakai, Javier Tejel, Jorge Urrutia
- Graphs and Combinatorics
- 2015

1 Let P be a set of n points in the plane in general position. A 2 subset H of P consisting of k elements that are the vertices of a convex 3 polygon is called a k-hole of P , if there is no element of P in the interior 4 of its convex hull. A set B of points in the plane blocks the k-holes of 5 P if any k-hole of P contains at least one element of B in the… (More)