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