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.

Doubly transitive 2-factorizations / Bonisoli, Arrigo; M., Buratti; Mazzuoccolo, Giuseppe. - In: JOURNAL OF COMBINATORIAL DESIGNS. - ISSN 1063-8539. - STAMPA. - 15:2(2007), pp. 120-132. [10.1002/jcd.20111]

Doubly transitive 2-factorizations

BONISOLI, Arrigo;MAZZUOCCOLO, Giuseppe
2007

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.
2007
15
2
120
132
Doubly transitive 2-factorizations / Bonisoli, Arrigo; M., Buratti; Mazzuoccolo, Giuseppe. - In: JOURNAL OF COMBINATORIAL DESIGNS. - ISSN 1063-8539. - STAMPA. - 15:2(2007), pp. 120-132. [10.1002/jcd.20111]
Bonisoli, Arrigo; M., Buratti; Mazzuoccolo, Giuseppe
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/613661
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