منابع مشابه
Witness Gabriel graphs
We consider a generalization of the Gabriel graph, the witness Gabriel graph. Given a set of vertices P and a set of witness points W in the plane, there is an edge ab between two points of P in the witness Gabriel graph GG−(P,W ) if and only if the closed disk with diameter ab does not contain any witness point (besides possibly a and/or b). We study several properties of the witness Gabriel g...
متن کاملRelaxed Gabriel Graphs
We study a new family of geometric graphs that interpolate between the Delaunay triangulation and the Gabriel graph. These graphs share many properties with βskeletons for β ∈ [0, 1] (such as sublinear spanning ratio) with the added benefit of planarity (and consequently linear size and local routability).
متن کاملMatching in Gabriel Graphs
Given a set P of n points in the plane, the order-k Gabriel graph on P , denoted by k-GG, has an edge between two points p and q if and only if the closed disk with diameter pq contains at most k points of P , excluding p and q. We study matching problems in k-GG graphs. We show that a Euclidean bottleneck perfect matching of P is contained in 10-GG, but 8-GG may not have any Euclidean bottlene...
متن کاملOn Locally Gabriel Geometric Graphs
Let P be a set of n points in the plane. A geometric graph G on P is said to be locally gabriel if for every edge (u, v) in G, the disc with u and v as diameter does not contain any points of P that are neighbors of u or v in G. Motivated by applications in topology control of wireless networks, [KL03] initiated the study of this graph. An interesting combinatorial question is to bound the edge...
متن کامل10-Gabriel graphs are Hamiltonian
Given a set S of points in the plane, the k-Gabriel graph of S is the geometric graph with vertex set S, where pi, pj ∈ S are connected by an edge if and only if the closed disk having segment pipj as diameter contains at most k points of S \ {pi, pj}. We consider the following question: What is the minimum value of k such that the k-Gabriel graph of every point set S contains a Hamiltonian cyc...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2013
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2011.06.004