Geodesic
Homogeneous factorisations of complete graphs with edge-transitive factors
Journal of Algebraic Combinatorics, Tome 29 (2009) no. 1, pp. 107-132.

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Summary: A factorisation of a complete graph $K _{ n }$ is a partition of its edges with each part corresponding to a spanning subgraph (not necessarily connected), called a factor. A factorisation is called homogeneous if there are subgroups $M G\leq S _{ n }$ such that $M$ is vertex-transitive and fixes each factor setwise, and $G$ permutes the factors transitively. We classify the homogeneous factorisations of $K _{ n }$ for which there are such subgroups $G, M$ with $M$ transitive on the edges of a factor as well as the vertices. We give infinitely many new examples.
Classification : !!par!!, Another, link, with, previous, work, is, to, the, partial, classification, by, Thomas, Sibley, [29], of, decompositions, of, complete, graphs, into, isomorphic, subgraphs, (not, nec-
Keywords: keywords graph factorisation, edge-transitive graph, homogeneous factorisation 
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Li, Cai Heng; Lim, Tian Khoon; Praeger, Cheryl E. Homogeneous factorisations of complete graphs with edge-transitive factors. Journal of Algebraic Combinatorics, Tome 29 (2009) no. 1, pp. 107-132. http://geodesic.mathdoc.fr/item/JAC_2009__29_1_a0/