Spanning trees with specified differences in Cayley graphs

If G is a finite group of order n , we denote by K G the complete Cayley graph on G . Let L be a multiset of group elements of G . If K G contains a subgraph whose edge labels are precisely L then we say that L is realizable as a G -subgraph. For an arbitrary finite group G , we present necessary and sufficient conditions for a multiset L to be realizable as a G -spanning tree and an algorithm for finding such a tree. This work is motivated by a problem posed by Marco Buratti on Hamiltonian paths in prime order complete graphs.