Now showing items 1-5 of 5

• #### Note on the number of obtuse angles in point sets ﻿

(2014-09)
Article
Open Access
In $1979$ 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 cross-sections of line arrangements in R^3 ﻿

(2014)
Conference report
Restricted access - publisher's policy
We 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 ﻿

(2017)
Conference report
Open Access
Let 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 ﻿

(University of Ljubljana, 2015)
Conference report
Restricted access - publisher's policy
We 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 straight-line segments. We define the empty ...
• #### The number of empty four-gons in random point sets ﻿

(2014)
Article
Open Access
Let S be a set of n points distributed uniformly and independently in the unit square. Then the expected number of empty four-gons with vertices from S is T(n^2 log¿ n). A four-gon is empty if it contains no points of S ...