Now showing items 1-8 of 8

• #### A polynomial bound for untangling geometric planar graphs ﻿

(2009-12)
Article
Open Access
To untangle a geometric graph means to move some of the vertices so that the resulting geometric graph has no crossings. Pach and Tardos (Discrete Comput. Geom. 28(4): 585–592, 2002) asked if every n-vertex geometric planar ...
• #### Connectivity-preserving transformations of binary images ﻿

(2009-10)
Article
Open Access
A binary image $\emph{I}$ is $B_a$, $W_b$-connected, where $\emph{a,b}$ ∊ {4,8}, if its foreground is $\emph{a}$-connected and its background is $\emph{b}$-connected. We consider a local modification of a $B_a$, $W_b$-connected ...
• #### Every large point set contains many collinear points or an empty pentagon ﻿

(2011-01)
Article
Restricted access - publisher's policy
We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next ...
• #### On computing enclosing isosceles triangles and related problems ﻿

(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 structural and graph theoretic properties of higher order Delaunay graphs ﻿

(2009-12)
Article
Open Access
Given a set $\emph{P}$ of $\emph{n}$ points in the plane, the order-$\emph{k}$ Delaunay graph is a graph with vertex set $\emph{P}$ and an edge exists between two points p,q ∊ $\emph{P}$ when there is a circle through ...
• #### Pole Dancing: 3D Morphs for Tree Drawings ﻿

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 ...
• #### 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 ...
• #### Some properties of higher order delaunay and gabriel graphs ﻿

(2010)
Conference report
Open Access
We consider two classes of higher order proximity graphs defined on a set of points in the plane, namely, the k-Delaunay graph and the k-Gabriel graph. We give bounds on the following combinatorial and geometric properties ...