Now showing items 1-12 of 12

• #### Affine invariant triangulations ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(Universitat Politècnica de Catalunya, 2020-06-25)
Doctoral thesis
Open Access
Covenantee:   Carleton University
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 ﻿

(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 ﻿

(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 ...
• #### Hamiltonicity for convex shape Delaunay and Gabriel Graphs ﻿

(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. ...
• #### Pole Dancing: 3D Morphs for Tree Drawings ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ...