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A transitive decomposition of a graph is a partition of the edge or arc setgiving a set of subgraphs which are preserved and permuted transitively by agroup of automorphisms of the graph. In this paper we give some background tothe study of transitive decompositions and highlight a connection with partiallinear spaces. We then describe a simple method for constructing transitivedecompositions using graph quotients, and we show how this may be used in anapplication to modular origami.

Transitive decompositions of graphs and their links with geometry and origami