Ruy Fabila-Monroy

Learn More
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)
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)
  • 1