We consider k-factorizations of the complete graph that are 1-rotational under an assigned group G, namely that admit G as an automorphism group acting sharply transitively on all but one vertex. After proving that the k-factors of such a factorization are pairwise isomorphic, we focus our attention to the special case k=2, a case in which we prove the involutions of G necessarily form a unique conjugacy class. We completely characterize, in particular, the 2-factorizations that are 1-rotational under a dihedral group. Finally, we get infinite new classes of prviously unknown solutions to the Oberwolfach problem via some direct and recursive constructions.

1-Rotational k-Factorizations of the Complete Graph and New Solutions to the Oberwolfach Problem / Buratti, M; Rinaldi, Gloria. - In: JOURNAL OF COMBINATORIAL DESIGNS. - ISSN 1063-8539. - STAMPA. - 16:2(2008), pp. 87-100. [10.1002/jcd.20163]

1-Rotational k-Factorizations of the Complete Graph and New Solutions to the Oberwolfach Problem

RINALDI, Gloria
2008

Abstract

We consider k-factorizations of the complete graph that are 1-rotational under an assigned group G, namely that admit G as an automorphism group acting sharply transitively on all but one vertex. After proving that the k-factors of such a factorization are pairwise isomorphic, we focus our attention to the special case k=2, a case in which we prove the involutions of G necessarily form a unique conjugacy class. We completely characterize, in particular, the 2-factorizations that are 1-rotational under a dihedral group. Finally, we get infinite new classes of prviously unknown solutions to the Oberwolfach problem via some direct and recursive constructions.
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1-Rotational k-Factorizations of the Complete Graph and New Solutions to the Oberwolfach Problem / Buratti, M; Rinaldi, Gloria. - In: JOURNAL OF COMBINATORIAL DESIGNS. - ISSN 1063-8539. - STAMPA. - 16:2(2008), pp. 87-100. [10.1002/jcd.20163]
Buratti, M; Rinaldi, Gloria
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/457908
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