Now showing items 1-12 of 12

    • Affine invariant triangulations 

      Bose, Prosenjit; Cano Vila, María del Pilar; Silveira, Rodrigo Ignacio (2019)
      Conference report
      Restricted access - publisher's policy
      We study affine invariant 2D triangulation methods. That is, methods that produce the same triangulation for a point set S for any (unknown) affine transformation of S. Our work is based on a method by Nielson [A ...
    • Compatible Paths on Labelled Point Sets 

      Arseneva, Elena; Bahoo, Yeganeh; Biniaz, Ahmad; Cano Vila, María del Pilar; Chanchary, Farah; Iacono, John; Jain, Kshitij; Lubiw, Anna; Mondal, Debajyoti; Sheikhan, Khadijeh; D. Thót, Csaba (2019)
      Conference report
      Open Access
      Let P and Q be finite point sets of the same cardinality in R 2 , each labelled from 1 to n. Two noncrossing geometric graphs GP and GQ spanning P and Q, respectively, are called compatible if for every face f in GP , there ...
    • Flips in higher order Delaunay triangulations 

      Arseneva, Elena; Bose, Prosenjit; Cano Vila, María del Pilar; Silveira, Rodrigo Ignacio (2021)
      Conference report
      Restricted access - publisher's policy
      We study the flip graph of higher order Delaunay triangulations. A triangulation of a set S of n points in the plane is order-k Delaunay if for every triangle its circumcircle encloses at most k points of S. The flip graph ...
    • Generalized Delaunay triangulations : graph-theoretic properties and algorithms 

      Cano Vila, María del Pilar (Universitat Politècnica de Catalunya, 2020-06-25)
      Doctoral thesis
      Open Access
      This thesis studies different generalizations of Delaunay triangulations, both from a combinatorial and algorithmic point of view. The Delaunay triangulation of a point set S, denoted DT(S), has vertex set S. An edge uv ...
    • Hamiltonicity for convex shape Delaunay and Gabriel Graphs 

      Bose, Prosenjit; Cano Vila, María del Pilar; Saumell Mendiola, Maria; Silveira, Rodrigo Ignacio (Springer, 2019)
      Conference report
      Restricted access - publisher's policy
      We study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Instead of defining these proximity graphs using circles, we use an arbitrary convex shape C. Let S be a point set in the plane. ...
    • Hamiltonicity for convex shape Delaunay and Gabriel graphs 

      Bose, Prosenjit; Cano Vila, María del Pilar; Saumell Mendiola, Maria; Silveira, Rodrigo Ignacio (2019)
      Conference report
      Restricted access - publisher's policy
      We study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Let S be a point set in the plane. The k-order Delaunay graph of S, denoted k-DGC(S), has vertex set S and edge pq provided ...
    • Hamiltonicity for convex shape Delaunay and Gabriel graphs 

      Bose, Prosenjit; Cano Vila, María del Pilar; Saumell Mendiola, Maria; Silveira, Rodrigo Ignacio (2020-08)
      Article
      Open Access
      We study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Instead of defining these proximity graphs using circles, we use an arbitrary convex shape \(\mathcal {C}\) . Let S be a point ...
    • Pole Dancing: 3D Morphs for Tree Drawings 

      Arseneva, Elena; Bose, Prosenjit; Cano Vila, María del Pilar; D'Angelo, Anthony; Dujmovic, Vida; Frati, Fabrizio; Langerman, Stefan; Tappini, Alessandra (Springer, 2018)
      Conference report
      Restricted access - publisher's policy
      We study the question whether a crossing-free 3D morph between two straight-line drawings of an n-vertex tree can be constructed consisting of a small number of linear morphing steps. We look both at the case in which the ...
    • Rainbow matchings in hypergraphs 

      Cano Vila, María del Pilar (Universitat Politècnica de Catalunya, 2015-10)
      Master thesis
      Open Access
      A rainbow matching in an edge colored multihypergraph is a matching consisting of edges with pairwise distinct colors. In this master thesis we give an overview of the results about having a rainbow matching in edge-colored ...
    • Rainbow perfect matchings in r-partite graph structures 

      Cano Vila, María del Pilar; Perarnau, Guillem; Serra Albó, Oriol (2016-10-03)
      Article
      Open Access
      A matching M in an edge–colored (hyper)graph is rainbow if each pair of edges in M have distinct colors. We extend the result of Erdos and Spencer on the existence of rainbow perfect matchings in the complete bipartite ...
    • Rainbow spanning subgraphs in bounded edge–colourings of graphs with large minimum degree 

      Cano Vila, María del Pilar; Perarnau Llobet, Guillem; Serra Albó, Oriol (2017-08-01)
      Article
      Open Access
      We study the existence of rainbow perfect matching and rainbow Hamiltonian cycles in edge–colored graphs where every color appears a bounded number of times. We derive asymptotically tight bounds on the minimum degree of ...
    • Sequences of spanning trees for L-infinity Delaunay triangulations 

      Bose, Prosenjit; Cano Vila, María del Pilar; Silveira, Rodrigo Ignacio (2018)
      Conference report
      Open Access
      We extend a known result about L2-Delaunay triangulations to L∞-Delaunay. Let TS be the set of all non-crossing spanning trees of a planar n-point set S. We prove that for each element T of TS, there exists a length-decreasing ...