Layered circle packings (Q2368356)

Authors' abstract: Given a bounded sequence of integers \(d_0, d_1, d_2, \ldots\), \(6\leq d_n\leq M\), there is an associated abstract triangulation created by building up layers of vertices so that vertices on the \(n\)th layer have degree \(d_n\). 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 packing given the defining sequence \(\{d_n\}\).