Spanning trees with specified differences in Cayley graphs

If GG is a finite group of order nn, we denote by KGKG the complete Cayley graph on GG. Let LL be a multiset of group elements of GG. If KGKG contains a subgraph whose edge labels are precisely LL then we say that LL is realizable as a GG-subgraph. For an arbitrary finite group GG, we present necessary and sufficient conditions for a multiset LL to be realizable as a GG-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.