Doubly transitive 2‐factorizations |
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Authors: | Arrigo Bonisoli Marco Buratti Giuseppe Mazzuoccolo |
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Institution: | 1. Dipartimento di Scienze Sociali, Cognitive e Quantitative, Università di Modena e Reggio Emilia, via Allegri 9, 42100 Reggio Emilia, Italy;2. Dipartimento di Matematica e Informatica, Università di Perugia, via Vanvitelli 1, 06123 Perugia, Italy;3. Dipartimento di Matematica, Università di Modena e Reggio Emilia, via Campi 213/B, 41100 Modena, Italy |
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Abstract: | Let be a 2‐factorization of the complete graph Kv admitting an automorphism group G acting doubly transitively on the set of vertices. The vertex‐set V(Kv) can then be identified with the point‐set of AG(n, p) and each 2‐factor of is the union of p‐cycles which are obtained from a parallel class of lines of AG(n, p) in a suitable manner, the group G being a subgroup of A G L(n, p) in this case. The proof relies on the classification of 2‐(v, k, 1) designs admitting a doubly transitive automorphism group. The same conclusion holds even if G is only assumed to act doubly homogeneously. © 2006 Wiley Periodicals, Inc. J Combin Designs |
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Keywords: | graph 2‐factorization doubly transitive permutation group design |
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