Some properties of higher order delaunay and gabriel graphs
نویسندگان
چکیده
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 of these graphs: spanning ratio, diameter, chromatic number, and minimum number of layers necessary to partition the edges of the graphs so that no two edges of the same layer cross.
منابع مشابه
Some properties of k-Delaunay and k-Gabriel graphs
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 of these graphs: spanning ratio, diameter, connectivity, chromatic number, and minimum number of layers necessary to partition the edges of the graphs so that no two edges of...
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 کاملOn Structural and Graph Theoretic Properties of Higher Order Delaunay Graphs
Given a set P of n points in the plane, the order-k Delaunay graph is a graph with vertex set P and an edge exists between two points p, q ∈ P when there is a circle through p and q with at most k other points of P in its interior. We provide upper and lower bounds on the number of edges in an order-k Delaunay graph. We study the combinatorial structure of the set of triangulations that can be ...
متن کاملProximity Graphs: E, Δ, Δ, Χ and Ω
Graph-theoretic properties of certain proximity graphs defined on planar point sets are investigated. We first consider some of the most common proximity graphs of the family of the Delaunay graph, and study their number of edges, minimum and maximum degree, clique number, and chromatic number. In the second part of the paper we focus on the higher order versions of some of these graphs and giv...
متن کاملOn crossing numbers of geometric proximity graphs
Let P be a set of n points in the plane. A geometric proximity graph on P is a graph where two points are connected by a straight-line segment if they satisfy some prescribed proximity rule. We consider four classes of higher order proximity graphs, namely, the k-nearest neighbor graph, the k-relative neighborhood graph, the k-Gabriel graph and the k-Delaunay graph. For k = 0 (k = 1 in the case...
متن کامل