We consider 2-factorizations of complete graphs that possess an automorphism group fixing k≥0 vertices and acting sharply transitively on the others. We study the structures of such factorizations and consider the cases in which the group is either abelian or dihedral in some more details. Combining results of the first part of the paper with a result of D. Bryant, J Combin Des, 12 (2004), 147–155, we prove that the class of 2-factorizations of complete graphs is universal. Namely each finite group is the full automorphism group of a 2-factorization of the class.
On 2-factorizations of the complete graph: from the k-pyramidal to the universal property
Mazzuoccolo, Giuseppe;
2009-01-01
Abstract
We consider 2-factorizations of complete graphs that possess an automorphism group fixing k≥0 vertices and acting sharply transitively on the others. We study the structures of such factorizations and consider the cases in which the group is either abelian or dihedral in some more details. Combining results of the first part of the paper with a result of D. Bryant, J Combin Des, 12 (2004), 147–155, we prove that the class of 2-factorizations of complete graphs is universal. Namely each finite group is the full automorphism group of a 2-factorization of the class.
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