Now showing items 1-20 of 26

• #### A finite point method for three-dimensional compressible flow ﻿

(2007-09)
External research report
Open Access
• #### 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 ...
• #### An explicit construction for neighborly centrally symmetric polytopes ﻿

(2006-06-29)
Article
Open Access
We give an explicit construction, based on Hadamard matrices, for an infinite series of $\big\lfloor\frac12\sqrt{d}\big\rfloor$-neighborly centrally symmetric $d$-dimensional polytopes with $4d$~vertices. This ...
• #### Approximation of a variable density cloud of points by shrinking a discrete membrane ﻿

(North Holland, 2005-12)
Article
Restricted access - publisher's policy
This paper describes a method to obtain a closed surface that approximates a general 3D data point set with nonuniform density. Aside from the positions of the initial data points, no other information is used. Particularly, ...
• #### Basis expansions and roots of Ehrhart polynomials ﻿

(2004)
Article
Open Access
• #### Bounding the volume of facet-empty lattice tetrahedra ﻿

(2005)
Article
Open Access
• #### Combinatorial properties of convex polygons in point sets ﻿

(Universitat Politècnica de Catalunya, 2019-07)
Master thesis
Open Access
The Erd&#337;s-Szekeres theorem is a famous result in Discrete geometry that inspired a lot of research and motivated new problems. The theorem states that for every integer n &#8805; 3 there is another integer N_0 such ...
• #### Combinatorial, geometric and probabilistic aspects of infinite sphere packings ﻿

(Universitat Politècnica de Catalunya, 2021-07)
Bachelor thesis
Open Access
This thesis focuses on the Circle Packing Theorem for graphs representations and how to relate it with the combinatorial structure of this mathematical objects. We will study the Koebe-Andreev-Thurston Theorem, a very ...
• #### Dissections, Hom-complexes and the Cayley trick ﻿

(2006-06-27)
Article
Open Access
We show that certain canonical realizations of the complexes $\Hom(G,H)$ and $\Hom_+(G,H)$ of (partial) graph homomorphisms studied by Babson and Kozlov are in fact instances of the polyhedral Cayley trick. For $G$~a ...
• #### Edge-superconnectivity of semiregular cages with odd girth ﻿

(Iniciativa Digital Politècnica, 2011)
Conference report
Open Access
A graph is said to be edge-superconnected if each minimum edge-cut consists of all the edges incident with some vertex of minimum degree. A graph G is said to be a {d, d + 1}- semiregular graph if all its vertices have ...
• #### 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 ...
• #### Exploiting symmetry on the Universal Polytope ﻿

(2012)
Conference report
Restricted access - publisher's policy
The most successful method to date for finding lower bounds on the number of simplices needed to triangulate a given polytope P involves optimizing a linear functional over the associated Universal Polytope U(P). However, ...
• #### Generalisation of Sylvester's problem ﻿

(Universitat Politècnica de Catalunya, 2015-09)
Bachelor thesis
Open Access
Let $P$ be a set of $n$ points in the projective space of dimension $d$ with the property that not all the points are contained in an hyperplane and any $d$ points span an hyperplane. Let an ordinary hyperplane of $P$ be ...
• #### Graphs with equal domination and 2-domination numbers ﻿

(Iniciativa Digital Politècnica, 2011)
Conference report
Open Access
For a graph G a subset D of the vertex set of G is a k-dominating set if every vertex not in D has at least k neighbors in D. The k-domination number γk(G) is the minimum cardinality among the k-dominating sets of G. Note ...
• #### Locomotion of self-organizing robots ﻿

(Universitat Politècnica de Catalunya, 2013-11)
Master thesis
Restricted access - author's decision
In our work we present a collection of distributed algorithms for the locomotion of rectangular and histogram-shaped square-lattice-based modular robots, on free ground and in the presence of obstacles. Each algorithm ...
• #### On identifying codes in partial linear spaces ﻿

(Iniciativa Digital Politècnica, 2011)
Conference report
Open Access
Let (P,L, I) be a partial linear space and X ⊆ P ∪ L. Let us denote by (X)I = x∈X{y : yIx} and by [X] = (X)I ∪ X. With this terminology a partial linear space (P,L, I) is said to admit a (1,≤ k)-identifying code if the ...
• #### On perfect and quasiperfect dominations in graphs ﻿

(2017-02-27)
Article
Open Access
A subset S ¿ V in a graph G = ( V , E ) is a k -quasiperfect dominating set (for k = 1) if every vertex not in S is adjacent to at least one and at most k vertices in S . The cardinality of a minimum k -quasiperfect ...
• #### On polytopality of Cartesian products of graphs ﻿

(2010-07)
Conference report
Open Access
We study the polytopality of Cartesian products of non-polytopal graphs. On the one hand, we prove that a product of graphs is the graph of a simple polytope if and only if its factors are. On the other hand, we provide ...
• #### On sets of points with few ordinary hyperplanes ﻿

(Universitat Politècnica de Catalunya, 2018-07)
Master thesis
Open Access
Let $S$ be a set of $n$ points in the projective $d$-dimensional real space $\mathbb{RP}^d$ such that not all points of $S$ are contained in a single hyperplane and such that any subset of $d$ points of $S$ span a hyperplane. ...
• #### On the connectivity and restricted edge-connectivity of 3-arc graphs ﻿

(Iniciativa Digital Politècnica, 2011)
Conference report
Open Access
A 3−arc of a graph G is a 4-tuple (y, a, b, x) of vertices such that both (y, a, b) and (a, b, x) are paths of length two in G. Let ←→G denote the symmetric digraph of a graph G. The 3-arc graph X(G) of a given graph G is ...