Now showing items 1-20 of 29

• #### Antimagic labelings of caterpillars ﻿

(2019-04-15)
Article
Restricted access - publisher's policy
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 ﻿

(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) ﻿

(2019-04)
Article
Restricted access - publisher's policy
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 ...
• #### Characteristic polynomials of production matrices for geometric graphs ﻿

(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 ...
• #### Extremal graph theory for metric dimension and diameter ﻿

(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 ...

(2010)
Article
Open Access
• #### Fitting a two-joint orthogonal chain to a point set ﻿

(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 ...
• #### Matching points with diametral disks ﻿

(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 things ﻿

(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 ...
• #### New results on stabbing segments with a polygon ﻿

(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 ...
• #### New results on stabbing segments with a polygon ﻿

(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 ...
• #### 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 geodetic sets formed by boundary vertices ﻿

(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 ...
• #### On Hamiltonian alternating cycles and paths ﻿

(2018-03)
Article
Open Access
We undertake a study on computing Hamiltonian alternating cycles and paths on bicolored point sets. This has been an intensively studied problem, not always with a solution, when the paths and cycles are also required to ...
• #### On monophonic sets in graphs ﻿

(2003)
External research report
Open Access
• #### On the determining number and the metric dimension of graphs ﻿

(2010-04-19)
Article
Open Access
This paper initiates a study on the problem of computing the difference between the metric dimension and the determining number of graphs. We provide new proofs and results on the determining number of trees and Cartesian ...
• #### On the Steiner, geodetic and hull numbers of graphs ﻿

(2003)
Article
Open Access
Given a graph G and a subset W ? V (G), a Steiner W-tree is a tree of minimum order that contains all of W. Let S(W) denote the set of all vertices in G that lie on some Steiner W-tree; we call S(W) the Steiner interval ...
• #### Production matrices for geometric graphs ﻿

(2016)
Article
Open Access
We present production matrices for non-crossing geometric graphs on point sets in convex position, which allow us to derive formulas for the numbers of such graphs. Several known identities for Catalan numbers, Ballot ...
• #### Some structural, metric and convex properties of the boundary of a graph ﻿

(2013-04-25)
Article
Open Access
Let u;v be two vertices of a connected graph G . The vertex v is said to be a boundary vertex of u if no neighbor of v is further away from u than v . The boundary of a graph is the set of all its ...
• #### Stabbers of line segments in the plane ﻿

(2011-07)
Article
Open Access
The problem of computing a representation of the stabbing lines of a set S of segments in the plane was solved by Edelsbrunner et al. We provide efficient algorithms for the following problems: computing the stabbing wedges ...