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- Bernardo M. Ábrego, Mario Cetina, Silvia Fernández-Merchant, Jesús Leaños, Gelasio Salazar
- Discrete Applied Mathematics
- 2010

Even the most superficial glance at the vast majority of crossing-minimal geometric drawings of Kn reveals two hard-to-miss features. First, all such drawings appear to be 3-fold symmetric (or simply… (More)

We describe the relationship between the crossing number of a graph G with a 2-edge-cut C and the crossing numbers of the components of G− C. Let G be a connected graph with a 2-edge-cut C := [V1,… (More)

- Bernardo M. Ábrego, Silvia Fernández-Merchant, Jesús Leaños, Gelasio Salazar
- Electronic Notes in Discrete Mathematics
- 2008

A generalized configuration is a set of n points and (n 2 ) pseudolines such that each pseudoline passes through exactly two points, two pseudolines intersect exactly once, and no three pseudolines… (More)

- Bernardo M. Ábrego, Silvia Fernández-Merchant, Jesús Leaños, Gelasio Salazar
- Electronic Notes in Discrete Mathematics
- 2008

For n ≤ 27 we present exact values for the maximum number h(n) of halving lines and h̃(n) of halving pseudolines, determined by n points in the plane. For this range of values of n we also present… (More)

Let P be a simple polygon on the plane. Two vertices of P are visible if the open line segment joining them is contained in the interior of P . In this paper we study the following questions posed in… (More)

On ( ≤ k ) – pseudoedges in generalized configurations and the pseudolinear crossing number of K n B

- . Ábrego, József Balogh, Jesús Leaños, Gelasio Salazar
- 2006

It is known that every generalized configuration with n points has at least 3 ` k+2 2 ́ (≤ k)–pseudoedges, and that this bound is tight for k ≤ n/3− 1. Here we show that this bound is no longer tight… (More)

- Jesús Leaños, Mario Lomelí, Criel Merino, Gelasio Salazar, Jorge Urrutia
- Discrete & Computational Geometry
- 2007

It is shown that if a simple Euclidean arrangement of n pseudolines has no (≥ 5)–gons, then it has exactly n − 2 triangles and (n − 2)(n − 3)/2 quadrilaterals. We also describe how to construct all… (More)

- Bernardo M. Ábrego, Mario Cetina, Jesús Leaños, Gelasio Salazar
- Inf. Process. Lett.
- 2012

Devadoss asked: (1) can every polygon be convexified so that no internal visibility (between vertices) is lost in the process? Moreover, (2) does such a convexification exist, in which exactly one… (More)

We present the latest developments on the number of (≤ k)-sets and halving lines for (generalized) configurations of points; as well as the rectilinear and pseudolinear crossing numbers of Kn. In… (More)

- Mario Cetina, César Hernández-Vélez, Jesús Leaños, C. Villalobos
- Discrete Mathematics
- 2011