Geodesic
On elementary moves that generate all spherical latin trades
Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 4, pp. 477-511.

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We show how to generate all spherical latin trades by elementary moves from a base set. If the base set consists only of a single trade of size four and the moves are applied only to one of the mates, then three elementary moves are needed. If the base set consists of all bicyclic trades (indecomposable latin trades with only two rows) and the moves are applied to both mates, then one move suffices. Many statements of the paper pertain to all latin trades, not only to spherical ones.
Classification : 05B15
Keywords: latin trade; spherical latin bi-trade; planar Eulerian triangulation 
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Drápal, Aleš. On elementary moves that generate all spherical latin trades. Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 4, pp. 477-511. http://geodesic.mathdoc.fr/item/CMUC_2009__50_4_a0/