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On k-enclosing objects in a coloured point set
(2014)
Text en actes de congrés.
Accés obert
Text en actes de congrés.
Accés obert
We introduce the exact coloured
k
-enclosing object
problem: given a set
P
of
n
points in
R
2
, each of
which has an associated colour in
f
1
;:::;t
g
, and a vec-
tor
c
= (
c
1
;:::;c
t
), ...
On the disks with diameters the sides of a convex 5-gon
(Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II (MA2), 2015)
Text en actes de congrés.
Accés restringit per política de l'editorial
Text en actes de congrés.
Accés restringit per política de l'editorial
We prove that for any convex pentagon there are two disks, among the five disks having a side of the pentagon as diameter and the midpoint of the side as its center, that do not intersect. This shows that K5 is never the ...
Matching points with diametral disks
(2017)
Text en actes de congrés.
Accés obert
Text en actes de congrés.
Accés obert
We consider matchings between a set R of red points and a set B of blue points with diametral disks. In other words, for each pair of matched points p ¿ R and q ¿ B, we consider the diametral disk defined by p and q. We ...
On k-gons and k-holes in point sets
(2015-08-01)
Article.
Accés obert
Article.
Accés obert
We consider a variation of the classical Erdos-Szekeres problems on the existence and number of convex k-gons and k-holes (empty k-gons) in a set of n points in the plane. Allowing the k-gons to be non-convex, we show ...
On the determining number and the metric dimension of graphs
(2010-04-19)
Article.
Accés obert
Article.
Accés obert
This paper initiates a study on the problem of computing the difference between
the metric dimension and the determining number of graphs. We provide new proofs
and results on the determining number of trees and Cartesian ...
Geometric biplane graphs II: graph augmentation
(2015-03-01)
Article.
Accés obert
Article.
Accés obert
We study biplane graphs drawn on a finite point set in the plane in general position. This is the family of geometric graphs whose vertex set is and which can be decomposed into two plane graphs. We show that every ...
Compatible spanning trees
(2014-07-01)
Article.
Accés obert
Article.
Accés obert
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 ...
New results on stabbing segments with a polygon
(Springer, 2013)
Text en actes de congrés.
Accés restringit per política de l'editorial
Text en actes de congrés.
Accés restringit per política de l'editorial
We consider a natural variation of the concept of stabbing a segment by a simple polygon: a segment is stabbed by a simple polygon P if at least one of its two endpoints is contained in P. A segment set S is stabbed by P ...
Stabbing circles for some sets of Delaunay segments
(2016)
Text en actes de congrés.
Accés obert
Text en actes de congrés.
Accés obert
Let S be a set of n segments in the plane such that, for
every segment, its two endpoints are adjacent in the Delaunay triangulation of the set of endpoints of all segments in S. Our goal is to compute all the combinatorially ...
Generalizing the Steiner-Lehmus theorem using the Gröbner cover
(2014-10-01)
Article.
Accés restringit per política de l'editorial
Article.
Accés restringit per política de l'editorial
In this note we present an application of a new tool (the Gröbner cover method, to discuss parametric polynomial systems of equations) in the realm of automatic discovery of theorems in elementary geometry. Namely, we ...