Hamiltonian decomposition of Cayley graphs of orders \(p^2\) and \(pq\) (Q1568238)
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scientific article; zbMATH DE number 1462497
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hamiltonian decomposition of Cayley graphs of orders \(p^2\) and \(pq\) |
scientific article; zbMATH DE number 1462497 |
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Hamiltonian decomposition of Cayley graphs of orders \(p^2\) and \(pq\) (English)
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13 June 2001
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A Hamiltonian decomposition of a graph is a decomposition of its edge set into (pairwise disjoint) Hamiltonian cycles. In this paper, the authors prove that every connected Cayley graph on an abelian group of order \(pq\) or \(p^2\) has a Hamiltonian decomposition, if \(p\) and \(q\) are odd prime numbers. This result answers partially a conjecture of Alspach concerning Hamiltonian decompositions of \(2k\)-regular Cayley graphs on abelian groups.
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Hamiltonian decomposition
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Hamiltonian cycles
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Cayley graph
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conjecture of Alspach
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