A Family of Perfect Factorisations of Complete Bipartite Graphs
A 1-factorisation of a graph is perfect if the union of any two of its 1-factors is a Hamiltonian cycle. Let n=p2 for an odd prime p. We construct a family of (p−1)/2 non-isomorphic perfect 1-factorisations of Kn, n. Equivalently, we construct pan-Hamiltonian Latin squares of order n. A Latin square...
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Veröffentlicht in: | Journal of combinatorial theory. Series A 2002-05, Vol.98 (2), p.328-342 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Online-Zugang: | Volltext |
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Zusammenfassung: | A 1-factorisation of a graph is perfect if the union of any two of its 1-factors is a Hamiltonian cycle. Let n=p2 for an odd prime p. We construct a family of (p−1)/2 non-isomorphic perfect 1-factorisations of Kn, n. Equivalently, we construct pan-Hamiltonian Latin squares of order n. A Latin square is pan-Hamiltonian if the permutation defined by any row relative to any other row is a single cycle. |
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ISSN: | 0097-3165 1096-0899 |
DOI: | 10.1006/jcta.2001.3240 |