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Hamiltonian cycles in (2,3,c)-circulant digraphs. (English) Zbl 1229.05181

Summary: Let \(D\) be the circulant digraph with \(n\) vertices and connection set \(\{2,3,c\}\). (Assume \(D\) is loopless and has outdegree 3.) Work of S. C. Locke and D. Witte implies that if \(n\) is a multiple of 6, \(c\in \{(n/2)+2,(n/2)+3\}\), and \(c\) is even, then \(D\) does not have a hamiltonian cycle. For all other cases, we construct a hamiltonian cycle in \(D\).

MSC:

05C38 Paths and cycles
05C45 Eulerian and Hamiltonian graphs
05C20 Directed graphs (digraphs), tournaments
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References:

[1] Locke, Stephen C.; Witte, Dave, On non-hamiltonian circulant digraphs of outdegree three, J. Graph Theory, 30, 4, 319-331 (1999), MR1669452 · Zbl 0921.05035
[2] Rankin, R. A., A campanological problem in group theory, Proc. Cambridge Philos. Soc., 44, 17-25 (1948), MR0022846 · Zbl 0030.10606
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