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 ...

We study a problem about shortest paths in Delaunay triangulations. Given two nodes s, t in the Delaunay triangulation of a point set P, we look for a new point p that can be added, such that the shortest path from s to ...

Al llarg d'aquesta memòria, hem plantejat possibles mesures de regularitat, totes elles justificades, per a un n-gon convex qualsevol que han donat lloc a problemes de geometria discreta i computacional. A més, hem estat ...

Given a large weighted graph G = (V;E) and a subset U of V , we de¯ne several graphs with vertex set U in which two vertices are adjacent if they satisfy some prescribed proximity rule. These rules use the shortest path ...

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 ...