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Resumen In this paper we review recent results on a new variation of the Art Gallery problem. A common problem we face nowadays, is that of placing a set of wireless modems in a building in such a way that a computer placed anywhere within the building receives a signal strong enough to connect to the Web. In most buildings, the main limitation for this… (More)

- Crevel Bautista-Santiago, Javier Cano, +5 authors Jorge Urrutia
- 2015

We study a geometric Ramsey type problem where the vertices of the complete graph K n are placed on a set S of n points in general position in the plane, and edges are drawn as straight-line segments. We define the empty convex polygon Ramsey number R EC (k, k) as the smallest number n such that for every set S of n points and for every two-coloring of the… (More)

Let S be a 2-colored (red and blue) set of n points in the plane. A subset I of S is an island if there exits a convex set C such that I = C ∩S. The discrepancy of an island is the absolute value of the number of red minus the number of blue points it contains. A convex partition of S is a partition of S into islands with pairwise disjoint convex hulls. The… (More)

- Bernardo M. Ábrego, Ruy Fabila-Monroy, +4 authors Maria Saumell
- 2009

We study the number of crossings among edges of some higher order proximity graphs of the family of the Delaunay graph. That is, given a set P of n points in the Euclidean plane, we give lower and upper bounds on the minimum and the maximum number of crossings that these geometric graphs defined on P have.

We consider a variation of a problem stated by Erdös and Guy in 1973 about the number of convex k-gons determined by any set S of n points in the plane. In our setting the points of S are colored and we say that a spanned polygon is monochromatic if all its points are colored with the same color. As a main result we show that any bi-colored set of n points… (More)

This paper studies the chromatic number of the following four flip graphs (under suitable definitions of a flip): • the flip graph of perfect matchings of a complete graph of even order, • the flip graph of triangulations of a convex polygon (the associahedron), • the flip graph of non-crossing Hamiltonian paths of a convex point set, and • the flip graph… (More)

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