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]
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