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Spanning trees with specified differences in Cayley graphs. (English) Zbl 1246.05075
Summary: 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.

##### MSC:
 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 05C05 Trees 05C45 Eulerian and Hamiltonian graphs 05B35 Combinatorial aspects of matroids and geometric lattices
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##### References:
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