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Generation of simple quadrangulations of the sphere

Brinkmann, Gunnar; Greenberg, Sam; Greenhill, Catherine; McKay, Brendan; Thomas, Robin; Wollan, Paul


A simple quadrangulation of the sphere is a finite simple graph embedded on the sphere such that every face is bounded by a walk of 4 edges. We consider the following classes of simple quadrangulations: arbitrary, minimum degree 3, 3-connected, and 3-connected without non-facial 4-cycles. In each case, we show how the class can be generated by starting with some basic graphs in the class and applying a sequence of local modifications. The duals of our algorithms generate classes of quartic...[Show more]

CollectionsANU Research Publications
Date published: 2005
Type: Journal article
Source: Discrete Mathematics
DOI: 10.1016/j.disc.2005.10.005


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