International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 15, Pages 2429-2440

Layered circle packings

David Dennis and G. Brock Williams

Department of Mathematics and Statistics, Texas Tech University, Lubbock 79409-1042, TX, USA

Received 14 January 2005; Revised 23 June 2005

Copyright © 2005 David Dennis and G. Brock Williams. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Given a bounded sequence of integers {d0,d1,d2,}, 6dnM, 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}.