1. Primitive 2-factorizations of the complete graph
- Author
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Giuseppe Mazzuoccolo
- Subjects
Discrete mathematics ,Hypergraph ,Complete graph ,Outer automorphism group ,Hamiltonian path ,Theoretical Computer Science ,Graphs and groups ,Combinatorics ,symbols.namesake ,Coloring of graphs and hypergraphs ,Edge-transitive graph ,Inner automorphism ,Factorization ,symbols ,Discrete Mathematics and Combinatorics ,Isomorphism ,Graph automorphism ,Factorization, Coloring of graphs and hypergraphs, Graphs and groups ,Mathematics - 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 automorphism group which acts 2-transitively on the vertex-set, see [A. Bonisoli, M. Buratti, G. Mazzuoccolo, Doubly transitive 2-factorizations, J. Combin. Designs 15 (2007) 120–132.]. 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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