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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.

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