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Implementing datadependent triangulations with higher order delaunay triangulations
(Multidisciplinary Digital Publishing Institute (MDPI), 20171201)
Article
Restricted access  publisher's policyThe Delaunay triangulation is the standard choice for building triangulated irregular networks (TINs) to represent terrain surfaces. However, the Delaunay triangulation is based only on the 2D coordinates of the data points, ... 
Distance 2domination in prisms of graphs
(20170101)
Article
Open AccessA set of vertices D of a graph G is a distance 2dominating set of G if the distance between each vertex u ¿ ( V ( G )  D ) and D is at most two. Let ¿ 2 ( G ) denote the size of a smallest distance 2 dominating set of ... 
On Hamiltonian alternating cycles and paths
(201803)
Article
Open AccessWe 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 ... 
Carathodory's theorem in depth
(20170701)
Article
Open AccessLet X be a finite set of points in RdRd . The Tukey depth of a point q with respect to X is the minimum number tX(q)tX(q) of points of X in a halfspace containing q. In this paper we prove a depth version of Carathéodory’s ... 
Characteristic polynomials of production matrices for geometric graphs
(20170801)
Article
Open AccessAn 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 ... 
Internally perfect matroids
(20170616)
Article
Open AccessIn 1977 Stanley proved that the $h$vector of a matroid is an $\mathcal{O}$sequence and conjectured that it is a pure $\mathcal{O}$sequence. In the subsequent years the validity of this conjecture has been shown for a ... 
Stabbing segments with rectilinear objects
(20170915)
Article
Open AccessGiven a set S of n line segments in the plane, we say that a region R¿R2 is a stabber for S if R contains exactly one endpoint of each segment of S. In this paper we provide optimal or nearoptimal algorithms for ... 
On perfect and quasiperfect dominations in graphs
(20170227)
Article
Open AccessA subset S ¿ V in a graph G = ( V , E ) is a k quasiperfect dominating set (for k = 1) if every vertex not in S is adjacent to at least one and at most k vertices in S . The cardinality of a minimum k quasiperfect ... 
Stabbing circles for sets of segments in the plane
(20170313)
Article
Open AccessStabbing a set S of n segments in the plane by a line is a wellknown problem. In this paper we consider the variation where the stabbing object is a circle instead of a line. We show that the problem is tightly connected ... 
General properties of ccirculant digraphs
(1988)
Article
Open AccessA digraph is said to be a ccirculant if its adjacency matrix is ccirculant. This paper deals with general properties of this family of digraphs, as isomorphisms, regularity, strong connectivity, diameter and the relation ... 
Production matrices for geometric graphs
(2016)
Article
Open AccessWe present production matrices for noncrossing 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 ... 
New results on stabbing segments with a polygon
(20150101)
Article
Open AccessWe 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 ...