Jill Bigley Dunham

Extremal coin graphs on multiple radii

Abstract: In this talk, we will consider extremal coin graphs in the Euclidean plane. A coin graph is a graph whose vertices can be represented as the centers of closed, non-overlapping disks in the Euclidean plane such that two vertices are adjacent if and only if their corresponding disks are tangent. The problem of determining the maximum number of edges of a unit coin graph on n vertices has been solved previously by Heiko Harborth. We will generalize the problem to coin graphs with multiple possible radii in a couple of different ways. A motivating problem is a special case of a coin graph with two possible radii. Another motivating problem is a classical problem of tangent circles known as Soddy circles.