On 2‐factorizations of the complete graph: From the k‐pyramidal to the universal property |
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| Authors: | Simona Bonvicini Giuseppe Mazzuoccolo Gloria Rinaldi |
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| Affiliation: | 1. Dipartimento di Scienze e Metodi dell'Ingegneria, Università di Modena e Reggio Emilia, Via Amendola 2 (pad. Morselli), 42100 Reggio Emilia, Italy;2. Dipartimento di Matematica, Università di Modena e Reggio Emilia, via Campi 213/B, 41100 Modena, Italy |
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| 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. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 211‐228, 2009 |
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| Keywords: | 2‐factorizations complete graphs automorphism groups |
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