Layered circle packings

Abstract

Given a bounded sequence of integers {d0,d1,d2,…}, 6≤dn≤M, there is an associated abstract triangulation created by building up layers of vertices so that vertices on the nth layer have degree dn. This triangulation can be realized via a circle packing which fills either the Euclidean or the hyperbolic plane. We give necessary and sufficient conditions to determine the type of the packing given the defining sequence {dn}.