Some properties of continuous yao graph

Abstract

Given a set S of points in the plane and an angle 0 < θ ≤ 2π, the continuous Yao graph cY (θ) with vertex set S and angle θ defined as follows. For each p, q ∈ S, we add an edge from p to q in cY (θ) if there exists a cone with apex p and angular diameter θ such that q is the closest point to p inside this cone. In this paper, we prove that for 0 < θ 0, cY (θ) is not necessarily a self-approaching graph.