Abstract
In this article, we show that all quadrangulations of the sphere with minimum degree at least 3 can be constructed from the pseudo-double wheels, preserving the minimum degree at least 3, by a sequence of two kinds of transformations called “vertex-splitting” and “4-cycle addition.” We also consider such generating theorems for other closed surfaces. These theorems can be translated into those of 4-regular graphs on surfaces by taking duals. © 1999 John Wiley & Sons, In. J Graph Theory 30: 223–234, 1999
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