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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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[1] Capparelli, S.; Del Fra, A., Hamiltonian paths in the complete graph with edge-lengths 1, 2, 3, The electronic journal of combinatorics, 17, #R44, (2010) · Zbl 1215.05095
[2] Dinitz, J.H.; Janiszewski, S.R., On Hamiltonian paths with prescribed edge lengths in the complete graph, Bulletin of the institute of combinatorics and its applications, 57, 42-52, (2009) · Zbl 1214.05068
[3] Horak, P.; Rosa, A., On a problem of marco – buratti, The electronic journal of combinatorics, 16, 1, #R20, (2009) · Zbl 1183.05042
[4] Oxley, James G., Matroid theory, (2006), Oxford University Press USA · Zbl 1115.05001
[5] Rado, R., A theorem on independent relations, The quarterly journal of mathematics. Oxford. second series, 13, 83-89, (1942) · Zbl 0063.06369
[6] Schrijver, A.; Seymour, P., Spanning trees of different weights, DIMACS series in discrete mathematics and theoretical computer science, 1, 281-288, (1990) · Zbl 0734.05032
[7] Douglas West, Buratti’s conjecture. http://www.math.uiuc.edu/ west/regs/buratti.html (online; accessed 31.05.10).
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