Papers by Alberto Marquez
Discrete Mathematics & Theoretical Computer Science, 2013
Graph Theory International audience A set of vertices S is a determining set of a graph G if ever... more Graph Theory International audience A set of vertices S is a determining set of a graph G if every automorphism of G is uniquely determined by its action on S. The determining number of G is the minimum cardinality of a determining set of G. This paper studies the determining number of Kneser graphs. First, we compute the determining number of a wide range of Kneser graphs, concretely Kn:k with n≥k(k+1) / 2+1. In the language of group theory, these computations provide exact values for the base size of the symmetric group Sn acting on the k-subsets of 1,..., n. Then, we establish for which Kneser graphs Kn:k the determining number is equal to n-k, answering a question posed by Boutin. Finally, we find all Kneser graphs with fixed determining number 5, extending the study developed by Boutin for determining number 2, 3 or 4.
An analysis of the concentratlons of potassiurn, sodium. calcium. magnesiurn. tron, proteíns and ... more An analysis of the concentratlons of potassiurn, sodium. calcium. magnesiurn. tron, proteíns and fat, was made in the muscular tissue of the líned catftsh PseUliop laiystomajasciatLtm from the middle Orlnoco ínVenezuela, as a contribu tlon to the knowledge ofthe ecofisiology ofthe species and ofits importance from the nutritious point ofview. The salts were analyzed by Espectrofotometria ofAtomic AbsorpUon with fIame of air-acetylene and correction ofdeuterium bottom, using a tearn Perkin Elmer 3100 coupled with al1 automueslreador Perkin-Elmer ACE-51. The percentages of proteins and fa t were determined by the method ofWeede (Omcial Methods of Analysls,AOAC).An average 26,03 jo 5,08 pg/ g was determin d in tbe fron concentraUon. 387,05 jo 33,38pg/gin the concentration of calcium, 951,00 jo 236.04 pg/g In the concentraUon of magnesium, 1386,73 jo 47.39 pg/g in the concentration of sodiurn. and 11626.41 jo 365,23 pg/ g in the concentration of potassium. The average ín the concentratl...
The sequential extraction method SEDEX (sedimentary extraction) modificated by ANDERSON…
Total concentrations and chemical forms of metals in superficial sediments of the MiddleOrinoco w... more Total concentrations and chemical forms of metals in superficial sediments of the MiddleOrinoco were determined with acetic acid solution 25% (v/v)/HNO3: HCl: HClO4 (3:2:1) solution,atomic absorption spectrometry with air acetylene flame and cold vapor technique. Totalvalues ranged from 8871 to 116759 μgFeg-1, 102.45 a 469.44 μgMn g-1; 0.93 to 17.64 μgCu g-1;4.46 to 17.48 μgNi g-1; 2.46 to 9.61 μgCo g-1; 42.56 to 181.45 μgZn g-1; 1.29 to 8.76 μgCr g-1; 0.03to 0.74 μgCd g-1 and 0.001 to 7.88 μgPb g-1. The metals were found to be strongly associated with the residual fraction minerals, more resistant iron oxihidroxides, metallic sulfides, and organicmatter. The values ranged from 7.50-99.29% Fe; 7.75-66.34% Mn; 22.55-98.89% Zn; 22.85-91.36% Ni; 4.20-85.03% Cu; 16.76-85.48% Co; 12.56-95.49 Cr; 7.50-99.29% Pb; 2.03-85.48%Cd). The values of metals adsorbed in the surface of particles, associated with carbonates andthe reactive manganese oxihidróxidos varied from 0.04-1.97% Fe; 4.15-71.59...
We study a graph parameter related to resolving sets and metric dimension, namely the resolving n... more We study a graph parameter related to resolving sets and metric dimension, namely the resolving number, introduced by Chartrand, Poisson and Zhang. First, we establish an important difference between the two parameters: while computing the metric dimension of an arbitrary graph is known to be NP-hard, we show that the resolving number can be computed in polynomial time. We then relate the resolving number to classical graph parameters: diameter, girth, clique number, order and maximum degree. With these relations in hand, we characterize the graphs with resolving number 3 extending other studies that provide characterizations for smaller resolving number.
This paper deals with the maximum value of the difference between the determining number and the ... more This paper deals with the maximum value of the difference between the determining number and the metric dimension of a graph as a function of its order. Our technique requires to use locating-dominating sets, and perform an independent study on other functions related to these sets. Thus, we obtain lower and upper bounds on all these functions by means of very diverse tools. Among them are some adequate constructions of graphs, a variant of a classical result in graph domination and a polynomial time algorithm that produces both distinguishing sets and determining sets. Further, we consider specific families of graphs where the restrictions of these functions can be computed. To this end, we utilize two well-known objects in graph theory: k-dominating sets and matchings.
Applied Mathematics and Computation, 2014
We study the maximum value of the difference between the metric dimension and the determining num... more We study the maximum value of the difference between the metric dimension and the determining number of a graph as a function of its order. We develop a technique that uses functions related to locating-dominating sets to obtain lower and upper bounds on that maximum, and exact computations when restricting to some specific families of graphs. Our approach requires very diverse tools and connections with well-known objects in graph theory; among them: a classical result in graph domination by Ore, a Ramsey-type result by Erd} os and Szekeres, a polynomial time algorithm to compute distinguishing sets and determining sets of twin-free graphs, k-dominating sets, and matchings.
Lecture Notes in Computer Science, 2001
Graphical features on map, charts, diagrams and graph drawings usually must be annotated with tex... more Graphical features on map, charts, diagrams and graph drawings usually must be annotated with text labels in order to convey their meaning. In this paper we focus on a problem that arises when labeling schematized maps, e.g. for subway networks. We present algorithms for labeling points on a line with axis-parallel rectangular labels of equal height. Our aim is to maximize label size under the constraint that all points must be labeled. Even a seemingly strong simplification of the general point-labeling problem, namely to decide whether a set of points on a horizontal line can be labeled with sliding rectangular labels, turns out to be weakly NPcomplete. This is the first labeling problem that is known to belong to this class. We give a pseudo-polynomial time algorithm for it. In case of a sloping line points can be labeled with maximum-size square labels in O(n log n) time if four label positions per point are allowed and in O(n 3 log n) time if labels can slide. We also investigate rectangular labels.
Lecture Notes in Computer Science, 2008
We study problems that arise in the context of covering certain geometric objects (so-called seed... more We study problems that arise in the context of covering certain geometric objects (so-called seeds, e.g., points or disks) by a set of other geometric objects (a so-called cover, e.g., a set of disks or homothetic triangles). We insist that the interiors of the seeds and the cover elements are pairwise disjoint, but they can touch. We call the contact graph of a cover a cover contact graph (CCG). We are interested in two types of tasks: (a) deciding whether a given seed set has a connected CCG, and (b) deciding whether a given graph has a realization as a CCG on a given seed set. Concerning task (a) we give efficient algorithms for the case that seeds are points and covers are disks or triangles. We show that the problem becomes NP-hard if seeds and covers are disks. Concerning task (b) we show that it is even NP-hard for point seeds and disk covers (given a fixed correspondence between vertices and seeds).
Networks, 2007
The dilation-free graph of a planar point set S is a graph that spans S in such a way that the di... more The dilation-free graph of a planar point set S is a graph that spans S in such a way that the distance between two points in the graph is no longer than their planar distance. Metrically speaking, those graphs are equivalent to complete graphs; however they have far fewer edges when considering the Manhattan distance (we give here an upper bound on the number of saved edges). This article provides several theoretical, algorithmic, and complexity features of dilation-free graphs in the l 1-metric, giving several construction algorithms and proving some of their properties. Moreover, special attention is paid to the planar case due to its applications in the design of printed circuit boards.
Mathematics and Computers in Simulation, 2014
A new edge-based partition for triangle meshes is presented, the Seven Triangle Quasi-Delaunay pa... more A new edge-based partition for triangle meshes is presented, the Seven Triangle Quasi-Delaunay partition (7T-QD). The proposed partition joins together ideas of the Seven Triangle Longest-Edge partition (7T-LE), and the classical criteria for constructing Delaunay meshes. The new partition performs similarly compared to the Delaunay triangulation (7T-D) with the benefit of being more robust and with a cheaper cost in computation. It will be proved that in most of the cases the 7T-QD is equal to the 7T-D. In addition, numerical tests will show that the difference on the minimum angle obtained by the 7T-QD and by the 7T-D is negligible.
Mathematics and Computers in Simulation, 2009
The triangle longest-edge bisection constitutes an efficient scheme for refining a mesh by reduci... more The triangle longest-edge bisection constitutes an efficient scheme for refining a mesh by reducing the obtuse triangles, since the largest interior angles are subdivided. In this paper we specifically introduce a new local refinement for triangulations based on the longest-edge trisection, the 7-triangle longest-edge (7T-LE) local refinement algorithm. Each triangle to be refined is subdivided in seven sub-triangles by determining its longest edge. The conformity of the new mesh is assured by an automatic point insertion criterion using the oriented 1-skeleton graph of the triangulation and three partial division patterns.
International Journal of Computational Geometry & Applications, 2012
In this paper, we introduce a natural variation of the problem of computing all bichromatic inter... more In this paper, we introduce a natural variation of the problem of computing all bichromatic intersections between two sets of segments. Given two sets R and B of n points in the plane defining two sets of segments, say red and blue, we present an O(n2) time and space algorithm for solving the problem of reporting the set of segments of each color intersected by segments of the other color. We also prove that this problem is 3-Sum hard and provide some illustrative examples of several point configurations.
Information Processing Letters, 2014
Given a bicolored point set S, it is not always possible to construct a monochromatic geometric p... more Given a bicolored point set S, it is not always possible to construct a monochromatic geometric planar k-factor of S. We consider the problem of finding such a k-factor of S by using auxiliary points. Two types are considered: white points whose position is fixed, and Steiner points which have no fixed position. Our approach provides algorithms for constructing those k-factors, and gives bounds on the number of auxiliary points needed to draw a monochromatic geometric planar k-factor of S.
Finite Elements in Analysis and Design, 2008
A new triangle partition, the seven-triangle longest-edge partition, based on the trisection of t... more A new triangle partition, the seven-triangle longest-edge partition, based on the trisection of the edges is presented and the associated mesh quality improvement property, discussed. The seven-triangle longest-edge (7T-LE) partition of a triangle t is obtained by putting two equally spaced points per edge. After cutting off three triangles at the corners, the remaining hexagon is subdivided further by joining each point of the longest-edge of t to the base points of the opposite sub-triangle. Finally, the interior quadrangle is subdivided into two sub-triangles by the shortest diagonal. The self-improvement property of the 7T-LE partition is discussed, delimited and compared to the parallel property of the four-triangle longest-edge (4T-LE) partition. Global refinement strategies, combining longest-edge with self-similar partitions, are proposed, based on the theoretical geometrical properties.
European Journal of Combinatorics, 2013
A set of vertices S in a graph G is a resolving set for G if, for any two vertices u, v, there ex... more A set of vertices S in a graph G is a resolving set for G if, for any two vertices u, v, there exists x ∈ S such that the distances d(u, x) = d(v, x). In this paper, we consider the Johnson graphs J(n, k) and Kneser graphs K(n, k), and obtain various constructions of resolving sets for these graphs. As well as general constructions, we show that various interesting combinatorial objects can be used to obtain resolving sets in these graphs, including (for Johnson graphs) projective planes and symmetric designs, as well as (for Kneser graphs) partial geometries, Hadamard matrices, Steiner systems and toroidal grids.
Electronic Notes in Discrete Mathematics, 2009
We study the existence of monochromatic planar geometric k-factors on sets of red and blue points... more We study the existence of monochromatic planar geometric k-factors on sets of red and blue points. When it is not possible to find a k-factor we make use of auxiliary points: white points, whose position is given as a datum and which color is free; and Steiner points whose position and color is free. We present bounds on the number of white and/or Steiner points necessary and/or sufficient to draw a monochromatic planar geometric k-factor.
Discrete Applied Mathematics, 2013
This paper deals with three resolving parameters: the metric dimension, the upper dimension and t... more This paper deals with three resolving parameters: the metric dimension, the upper dimension and the resolving number. We first answer a question raised by Chartrand and Zhang asking for a characterization of the graphs with equal metric dimension and resolving number. We also solve in the affirmative a conjecture posed by Chartrand, Poisson and Zhang about the realization of the metric dimension and the upper dimension. Finally we prove that no integer a ≥ 4 is realizable as the resolving number of an infinite family of graphs.
Trazados ortogonales en el plano. Resultados generales y aproximacion por algoritmos geneticos
1] Departamento de Matematica Aplicada I, Universidad de Sevilla (Spain)
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Papers by Alberto Marquez