Browsing by Author "FabilaMonroy, Ruy"
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Note on the number of obtuse angles in point sets
FabilaMonroy, Ruy; Huemer, Clemens; Tramuns, Eulàlia (201409)
Article
Open AccessIn $1979$ Conway, Croft, Erd\H{o}s and Guy proved that every set $S$ of $n$ points in general position in the plane determines at least $\frac{n^3}{18}O(n^2)$ obtuse angles and also presented a special set of $n$ points ... 
Order types and crosssections of line arrangements in R^3
Aichholzer, Oswin; FabilaMonroy, Ruy; Hurtado Díaz, Fernando Alfredo; Pérez Lantero, Pablo; Ruiz Vargas, Andrés; Urrutia Galicia, Jorge; Vogtenhuber, Birgit (2014)
Conference report
Restricted access  publisher's policyWe consider sets L = {l1,...., ln} of n labeled lines in general position in R3, and study the order types of point sets fp1; : : : ; png that stem from the intersections of the lines in L with (directed) planes II, not ... 
Order types of random point sets can be realized with small integer coordinates
FabilaMonroy, Ruy; Huemer, Clemens (2017)
Conference report
Open AccessLet S := {p1, . . . , pn} be a set of n points chosen independently and uniformly at random from the unit square and let M be a positive integer. For every point pi = (xi , yi) in S, let p 0 i = (bMxic, bMyic). Let S 0 := ... 
Ramsey numbers for empty convex polygons
BautistaSantiago, Crevel; Cano, Javier; FabilaMonroy, Ruy; HidalgoToscano, Carlos; Huemer, Clemens; Leaños, Jesús; Sakai, Toshinori; Urrutia, Jorge (University of Ljubljana, 2015)
Conference report
Restricted access  publisher's policyWe study a geometric Ramsey type problem where the vertices of the complete graph Kn are placed on a set S of n points in general position in the plane, and edges are drawn as straightline segments. We define the empty ... 
The number of empty fourgons in random point sets
FabilaMonroy, Ruy; Huemer, Clemens; Mitsche, Dieter (2014)
Article
Open AccessLet S be a set of n points distributed uniformly and independently in the unit square. Then the expected number of empty fourgons with vertices from S is T(n^2 log¿ n). A fourgon is empty if it contains no points of S ...