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1-rotational k-factorizations of the complete graph and new solutions to the Oberwolfach problem

✍ Scribed by Marco Buratti; Gloria Rinaldi

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
149 KB
Volume
16
Category
Article
ISSN
1063-8539

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✦ Synopsis

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 of k = 2, a case in which we prove that 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 previously unknown solutions to the Oberwolfach problem via some direct and recursive constructions. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 87–100, 2008

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