19 citations · 36 across the 15 of their papers we have counts for
13 papers · 1 filter
The Euclidean -Matching Problem is NP-hard
José-Miguel Díaz-Báñez, Ruy Fabila-Monroy, José-Manuel Higes-López +3
Let be a complete edge-weighted graph on vertices. To each subset of vertices of assign the cost of the minimum spanning tree of the subset as its weight. Suppose that…
A Note on the -colored Crossing Ratio of Dense Geometric Graphs
Ruy Fabila-Monroy
A \emph{geometric graph} is a graph whose vertex set is a set of points in general position in the plane, and its edges are straight line segments joining these points. We show tha…
Empty Rainbow Triangles in -colored Point Sets
Ruy Fabila-Monroy, Daniel Perz, Ana Laura Trujillo-Negrete
Let be a set of points in general position in the plane. Suppose that each point of has been assigned one of possible colors and that there is the same number…
Chirotopes of Random Points in Space are Realizable on a Small Integer Grid
Jean Cardinal, Ruy Fabila-Monroy, Carlos Hidalgo-Toscano
We prove that with high probability, a uniform sample of points in a convex domain in can be rounded to points on a grid of step size proportional to $1/n^{d+1+ε…
On the 2-colored crossing number
Oswin Aichholzer, Ruy Fabila-Monroy, Adrian Fuchs +4
Let be a straight-line drawing of a graph. The rectilinear 2-colored crossing number of is the minimum number of crossings between edges of the same color, taken over all p…
Counting the Number of Crossings in Geometric Graphs
Frank Duque, Ruy Fabila-Monroy, César Hernández-Vélez +1
A geometric graph is a graph whose vertices are points in general position in the plane and its edges are straight line segments joining these points. In this paper we give an $O(n…