Now showing items 1-7 of 7

• #### Edge-Removal and Non-Crossing Configurations in Geometric Graphs ﻿

(2010)
Article
Open Access
A geometric graph is a graph G = (V;E) drawn in the plane, such that V is a point set in general position and E is a set of straight-line segments whose endpoints belong to V . We study the following extremal problem for ...
• #### Matching random colored points with rectangles ﻿

(Springer, 2020)
Conference report
Open Access
Let S[0,1]2 be a set of n points, randomly and uniformly selected. Let RB be a random partition, or coloring, of S in which each point of S is included in R uniformly at random with probability 1/2. We study the random ...
• #### Matching random colored points with rectangles ﻿

(Springer, 2023-03-14)
Article
Open Access
Given n > 0, let S ¿ [0,1]2 be a set of n points, chosen uniformly at random. Let R¿B be a random partition, or coloring, of S in which each point of S is included in R uniformly at random with probability 1/2. We study ...
• #### Modem illumination of monotone polygons ﻿

(2009)
Conference report
Open Access
We study a generalization of the classical problem of illumination of polygons. Instead of modeling a light source we model a wireless device whose radio signal can penetrate a given number k of walls. We call these ...
• #### On maximum-sum matchings of points ﻿

(Springer Nature, 2022-06-21)
Article
Open Access
Huemer et al. (Discrete Mathematics, 2019) proved that for any two point sets R and B with |R|=|B| , the perfect matching that matches points of R with points of B, and maximizes the total squared Euclidean distance of the ...
• #### On maximum-sum matchings of points ﻿

(2021)
Conference report
Restricted access - publisher's policy
Huemer et al. (Discrete Math., 2019) proved that for any two point sets R and B with |R| = |B|, the perfect matching that matches points of R with points of B, and maximizes the total squared Euclidean distance of the ...
• #### Proximity graphs inside large weighted graphs ﻿

(2010)
Conference report
Open Access
Given a large weighted graph G = (V;E) and a subset U of V , we de¯ne several graphs with vertex set U in which two vertices are adjacent if they satisfy some prescribed proximity rule. These rules use the shortest path ...