Now showing items 1-20 of 53

• #### A polynomial bound for untangling geometric planar graphs ﻿

(2009-12)
Article
Open Access
To untangle a geometric graph means to move some of the vertices so that the resulting geometric graph has no crossings. Pach and Tardos (Discrete Comput. Geom. 28(4): 585–592, 2002) asked if every n-vertex geometric planar ...
• #### Balanced partitions of 3-colored geometric sets in the plane ﻿

(2015)
Article
Open Access
Let SS be a finite set of geometric objects partitioned into classes or colors . A subset S'¿SS'¿S is said to be balanced if S'S' contains the same amount of elements of SS from each of the colors. We study several ...
• #### Blocking the k-holes of point sets in the plane ﻿

(2015-09)
Article
Open Access
Let P be a set of n points in the plane in general position. A subset H of P consisting of k elements that are the vertices of a convex polygon is called a k-hole of P, if there is no element of P in the interior of its ...
• #### Cell-paths in mono- and bichromatic line arrangements in the plane ﻿

(2014)
Conference report
Open Access
We show that in every arrangement of n red and blue lines | in general position and not all of the same color | there is a path through a linear number of cells where red and blue lines are crossed alternatingly (and no ...
• #### Colored Ray configurations ﻿

(2014)
Conference report
Open Access
We study the cyclic sequences induced at in nity by pairwise-disjoint colored rays with apices on a given bal- anced bichromatic point set, where the color of a ray is inherited from the color of its apex. We derive a lower ...
• #### Colored ray configurations ﻿

(2018-05)
Article
Open Access
We study the cyclic color sequences induced at infinity by colored rays with apices being a given balanced finite bichromatic point set. We first study the case in which the rays are required to be pairwise disjoint. We ...
• #### Colored spanning graphs for set visualization ﻿

(Springer, 2013)
Conference report
Open Access
We study an algorithmic problem that is motivated by ink minimization for sparse set visualizations. Our input is a set of points in the plane which are either blue, red, or purple. Blue points belong exclusively to the ...
• #### Colored spanning graphs for set visualization ﻿

(2018-03)
Article
Open Access
We study an algorithmic problem that is motivated by ink minimization for sparse set visualizations. Our input is a set of points in the plane which are either blue, red, or purple. Blue points belong exclusively to the ...
• #### Compatible matchings in geometric graphs ﻿

(Centre de Recerca Matemàtica, 2011)
Conference report
Open Access
Two non-crossing geometric graphs on the same set of points are compatible if their union is also non-crossing. In this paper, we prove that every graph G that has an outerplanar embedding admits a non-crossing perfect ...
• #### Compatible spanning trees ﻿

(2014-07-01)
Article
Open Access
Two plane geometric graphs are said to be compatible when their union is a plane geometric graph. Let S be a set of n points in the Euclidean plane in general position and let T be any given plane geometric spanning tree ...
• #### Configurations of non-crossing rays and related problems ﻿

(2016-04)
Article
Open Access
Let S be a set of n points in the plane and let R be a set of n pairwise non-crossing rays, each with an apex at a different point of S. Two sets of non-crossing rays R1R1 and R2R2 are considered to be different if the ...
• #### Connectivity-preserving transformations of binary images ﻿

(2009-10)
Article
Open Access
A binary image $\emph{I}$ is $B_a$, $W_b$-connected, where $\emph{a,b}$ ∊ {4,8}, if its foreground is $\emph{a}$-connected and its background is $\emph{b}$-connected. We consider a local modification of a $B_a$, $W_b$-connected ...
• #### Coverage with k-transmitters in the presence of obstacles ﻿

(Springer Verlag, 2010)
Conference report
Restricted access - publisher's policy
For a fixed integer k ≥ 0, a k-transmitter is an omnidirectional wireless transmitter with an infinite broadcast range that is able to penetrate up to k “walls”, represented as line segments in the plane. We develop lower ...
• #### Distance 2-domination in prisms of graphs ﻿

(2017-01-01)
Article
Open Access
A set of vertices D of a graph G is a distance 2-dominating set of G if the distance between each vertex u ¿ ( V ( G ) - D ) and D is at most two. Let ¿ 2 ( G ) denote the size of a smallest distance 2 -dominating set of ...
• #### 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 ...
• #### Every large point set contains many collinear points or an empty pentagon ﻿

(2011-01)
Article
Restricted access - publisher's policy
We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next ...
• #### GEOMETRIA DISCRETA I COMPUTACIONAL (Examen 1r quadrim) ﻿

(Universitat Politècnica de Catalunya, 2006-01-18)
Exam
• #### GEOMETRIA DISCRETA I COMPUTACIONAL (Examen 1r quadrim) ﻿

(Universitat Politècnica de Catalunya, 2003-12-11)
Exam