LAYERED CIRCLE PACKINGS

Given a bounded sequence of integers { d 0 , d 1 , d 2 , …}, 6 ≤ d n ≤ 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 the packing given the defining sequence { d n }.