Regular Oberwolfach Problems and Group Sequencings

نویسندگان

  • Gil Kaplan
  • Arieh Lev
  • Yehuda Roditty
چکیده

We deal with Oberwolfach factorizations of the complete graphs Kn and K n *, which admit a regular group of automorphisms. We show that the existence of such a factorization is equivalent to the existence of a certain difference sequence defined on the elements of the automorphism group, or to a certain sequencing of the elements of that group. In the particular case of a hamiltonian factorization of the directed graph Kn * which admits a regular group of automorphisms G ( |G|=n&1), we have that such a factorization exists if and only if G is sequenceable. We shall demonstrate how the mentioned above (difference) sequences may be used in the construction of such factorizations. We prove also that a hamiltonian factorization of the undirected graph Kn (n odd) which admits a regular group of automorphisms G ( |G|=(n&1) 2) exists if and only if n#3 (mod 4), without further restrictions on the structure of G. 2001 Academic Press

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عنوان ژورنال:
  • J. Comb. Theory, Ser. A

دوره 96  شماره 

صفحات  -

تاریخ انتشار 2001