The intersection graph of the disks with diameters the sides of a convex n-gon

摘要

Given a convex polygon of n sides, one can draw n disks (called side disks) where each disk has a different side of the polygon as diameter and the midpoint of the side as its center. The intersection graph of such disks is the undirected graph with vertices the n disks and two disks are adjacent if and only if they have a point in common. We introduce the study of this graph by proving that it is planar for every convex polygon. (C) 2019 Elsevier B.V. All rights reserved.