Now showing items 1-20 of 37

    • Antimagic labelings of caterpillars 

      Lozano Bojados, Antoni; Mora Giné, Mercè; Seara Ojea, Carlos (2019-04-15)
      Article
      Open Access
      A k-antimagic labeling of a graph G is an injection from E(G) to {1,2, ..., |E(G)|+k} such that all vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of the labels assigned to edges incident ...
    • Balanced partitions of 3-colored geometric sets in the plane 

      Bereg, Sergey; Hurtado Díaz, Fernando Alfredo; Kano, Mikio; Korman, Matias; Lara, Dolores; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio; Urrutia Galicia, Jorge; Verbeek, Kevin (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 ...
    • Capturing points with a rotating polygon (and a 3D extension) 

      Alegría Galicia, Carlos; Orden, David; Palios, Leonidas; Seara Ojea, Carlos; Urrutia Galicia, Jorge (2019-04)
      Article
      Open Access
      We study the problem of rotating a simple polygon to contain the maximum number of elements from a given point set in the plane. We consider variations of this problem where the rotation center is a given point or lies on ...
    • Caterpillars are antimagic 

      Lozano Bojados, Antoni; Mora Giné, Mercè; Seara Ojea, Carlos; Tey Carrera, Joaquín (2021-01-21)
      Article
      Restricted access - publisher's policy
      An antimagic labeling of a graph G is a bijection from the set of edges E(G) to {1,2,…,|E(G)|}, such that all vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of the labels assigned to the ...
    • Characteristic polynomials of production matrices for geometric graphs 

      Huemer, Clemens; Pilz, Alexander; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio (2017-08-01)
      Article
      Open Access
      An n×n production matrix for a class of geometric graphs has the property that the numbers of these geometric graphs on up to n vertices can be read off from the powers of the matrix. Recently, we obtained such production ...
    • Characterizations of some complexity classes between [theta sub 2 super p] and [delta sub 2 super p] 

      Castro Rabal, Jorge; Seara Ojea, Carlos (1990)
      External research report
      Open Access
      We give some characterizations of the classes P super NP [0(log super k n)]. First, we show that these classes are equal to classes AC super k-1 (N P). Second, we prove that they are also equivalent to some classes defined ...
    • Convex quadrangulations of bichromatic point sets 

      Pilz, Alexander; Seara Ojea, Carlos (2020-06-05)
      Article
      Restricted access - publisher's policy
      We consider quadrangulations of red and blue points in the plane where each face is convex and no edge connects two points of the same color. In particular, we show that the following problem is NP-hard: Given a finite set ...
    • Efficient computation of minimum-area rectilinear convex hull under rotation and generalizations 

      Alegría Galicia, Carlos; Orden Martin, David; Seara Ojea, Carlos; Urrutia Galicia, Jorge (Springer Nature, 2021-03)
      Article
      Restricted access - publisher's policy
      Let P be a set of n points in the plane. We compute the value of ¿¿[0,2p) for which the rectilinear convex hull of P, denoted by RHP(¿), has minimum (or maximum) area in optimal O(nlogn) time and O(n) space, improving the ...
    • Extremal graph theory for metric dimension and diameter 

      Hernando Martín, María del Carmen; Mora Giné, Mercè; Seara Ojea, Carlos; Wood, David (2010-02-22)
      Article
      Open Access
      A set of vertices S resolves a connected graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. Let ...
    • Extremal graph theory for metric dimension and diameter 

      Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Seara Ojea, Carlos; Wood, David (2010)
      Article
      Open Access
    • Fitting a two-joint orthogonal chain to a point set 

      Díaz-Báñez, José Miguel; López, Mario A.; Mora Giné, Mercè; Seara Ojea, Carlos; Ventura, Inmaculada (2011-04)
      Article
      Open Access
      We study the problem of fitting a two-joint orthogonal polygonal chain to a set S of n points in the plane, where the objective function is to minimize the maximum orthogonal distance from S to the chain. We show that this ...
    • K-1,K-3-covering red and blue points in the plane 

      Ábrego, Bernardo M.; Fernández Merchant, Silvia; Kano, Mikio; Orden, David; Pérez Lantero, Pablo; Seara Ojea, Carlos; Tejel Altarriba, Francisco Javier (Chapman & Hall/CRC, 2019-01-31)
      Article
      Open Access
      We say that a finite set of red and blue points in the plane in general position can be K1,3-covered if the set can be partitioned into subsets of size 4, with 3 points of one color and 1 point of the other color, in such ...
    • Matching points with diametral disks 

      Huemer, Clemens; Pérez-Lantero, Pablo; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio (2017)
      Conference report
      Open Access
      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 ...
    • Matching points with disks with a common intersection 

      Huemer, Clemens; Pérez Lantero, Pablo; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio (2019-07-01)
      Article
      Restricted access - publisher's policy
      We 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 ...
    • Matching points with things 

      Taslakian, Perouz; Seara Ojea, Carlos; Saumell Mendiola, Maria; Langerman, Stefan; Hurtado Díaz, Fernando Alfredo; Aloupis, Greg; Cardinal, Jean; Collette, Sébastien; Demaine, Erik D.; Demaine, Martin L.; Dulieu, Muriel; Fabila Monroy, Ruy; Hart, Vi (Springer Verlag, 2010)
      Conference report
      Restricted access - publisher's policy
      Given an ordered set of points and an ordered set of geometric objects in the plane, we are interested in finding a non-crossing matching between point-object pairs. We show that when the objects we match the points to ...
    • Matching random colored points with rectangles 

      Corujo, Josué; Flores Peñazola, David; Huemer, Clemens; Pérez Lantero, Pablo; Seara Ojea, Carlos (Universitat de Girona, 2019)
      Conference lecture
      Open Access
      Let S ¿ [0, 1]2 be a set of n points, randomly and uniformly selected. Let R ¿ B be a random partition, or coloring, of S in which each point of S is included in R uniformly at random with probability 1/2. We study the ...
    • New results on stabbing segments with a polygon 

      Díaz Bañez, José Miguel; Korman Cozzetti, Matías; Pérez Lantero, Pablo; Pilz, Alexander; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio (Springer, 2013)
      Conference report
      Restricted access - publisher's policy
      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 ...
    • New results on stabbing segments with a polygon 

      Díaz Bañez, José Miguel; Korman Cozzetti, Matías; Pérez Lantero, Pablo; Pilz, Alexander; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio (2015-01-01)
      Article
      Open Access
      We consider a natural variation of the concept of stabbing a set of segments with a simple polygon: a segment s is stabbed by a simple polygon P if at least one endpoint of s is contained in P, and a segment set S is stabbed ...
    • On computing enclosing isosceles triangles and related problems 

      Bose, Prosenjit; Mora Giné, Mercè; Seara Ojea, Carlos; Sethia, Saurabh (2011-02)
      Article
      Open Access
      Given a set of n points in the plane, we show how to compute various enclosing isosceles triangles where different parameters such as area or perimeter are optimized. We then study a 3-dimensional version of the problem ...
    • On geodetic sets formed by boundary vertices 

      Cáceres González, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas González, María Luz; Seara Ojea, Carlos (2003)
      Article
      Open Access
      Let G be a finite simple connected graph. A vertex v is a boundary vertex of G if there exists a vertex u such that no neighbor of v is further away from u than v. We obtain a number of properties involving different types ...