Let F be a 2-factorization of the complete graph Kv admitting an automorphism group G acting primitively on the set of vertices.If F consists of Hamiltonian cycles, then F is the unique, up to isomorphisms, 2-factorization of Kpn admitting an automorphismgroup which acts 2-transitively on the vertex-set. In the non-Hamiltonian case we construct an infinite family of examples whose automorphism group does not contain a subgroup acting 2-transitively on vertices.
Primitive 2-factorizations of the complete graph / Mazzuoccolo, Giuseppe. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - STAMPA. - 308:2-3(2008), pp. 175-179. [10.1016/j.disc.2006.02.017]
Primitive 2-factorizations of the complete graph
MAZZUOCCOLO, Giuseppe
2008
Abstract
Let F be a 2-factorization of the complete graph Kv admitting an automorphism group G acting primitively on the set of vertices.If F consists of Hamiltonian cycles, then F is the unique, up to isomorphisms, 2-factorization of Kpn admitting an automorphismgroup which acts 2-transitively on the vertex-set. In the non-Hamiltonian case we construct an infinite family of examples whose automorphism group does not contain a subgroup acting 2-transitively on vertices.
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