Browsing by Subject "Discrete geometry"
Now showing items 120 of 28

A finite point method for threedimensional compressible flow
(200709)
External research report
Open Access 
A polynomial bound for untangling geometric planar graphs
(200912)
Article
Open AccessTo 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 nvertex geometric planar ... 
An explicit construction for neighborly centrally symmetric polytopes
(20060629)
Article
Open AccessWe 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
(200212)
External research report
Open AccessThis paper describes a method to obtain a closed surface that approximates a general 3D data point set with nonuniform density. Excluding the initial data points, any other previous information is not used (as, for ... 
Approximation of a variable density cloud of points by shrinking a discrete membrane
(North Holland, 200512)
Article
Restricted access  publisher's policyThis 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 facetempty lattice tetrahedra
(2005)
Article
Open Access 
Combinatorial properties of convex polygons in point sets
(Universitat Politècnica de Catalunya, 201907)
Master thesis
Open AccessThe ErdősSzekeres 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 ≥ 3 there is another integer N_0 such ... 
Combinatorial, geometric and probabilistic aspects of infinite sphere packings
(Universitat Politècnica de Catalunya, 202107)
Bachelor thesis
Open AccessThis 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 KoebeAndreevThurston Theorem, a very ... 
Dissections, Homcomplexes and the Cayley trick
(20060627)
Article
Open AccessWe 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 ... 
Edgesuperconnectivity of semiregular cages with odd girth
(Iniciativa Digital Politècnica, 2011)
Conference report
Open AccessA graph is said to be edgesuperconnected if each minimum edgecut 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
(201101)
Article
Restricted access  publisher's policyWe 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 policyThe 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, 201509)
Bachelor thesis
Open AccessLet $P$ 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 2domination numbers
(Iniciativa Digital Politècnica, 2011)
Conference report
Open AccessFor a graph G a subset D of the vertex set of G is a kdominating set if every vertex not in D has at least k neighbors in D. The kdomination number γk(G) is the minimum cardinality among the kdominating sets of G. Note ... 
Locomotion of selforganizing robots
(Universitat Politècnica de Catalunya, 201311)
Master thesis
Restricted access  author's decisionIn our work we present a collection of distributed algorithms for the locomotion of rectangular and histogramshaped squarelatticebased modular robots, on free ground and in the presence of obstacles. Each algorithm ... 
Lower bounds for the number of small convex kholes
(20140701)
Article
Open AccessLet S be a set of n points in the plane in general position, that is, no three points of S are on a line. We consider an Erdostype question on the least number h(k)(n) of convex kholes in S, and give improved lower bounds ... 
Matching points with disks with a common intersection
(20190701)
Article
Open AccessWe consider matchings with diametral disks between two sets of points R and B. More precisely, for each pair of matched points p ¿ R and q ¿ B, we consider the disk through p and q with the smallest diameter. We prove that ... 
On identifying codes in partial linear spaces
(Iniciativa Digital Politècnica, 2011)
Conference report
Open AccessLet (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 polytopality of Cartesian products of graphs
(201007)
Conference report
Open AccessWe study the polytopality of Cartesian products of nonpolytopal 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 ...