Let F be a 2-factorization of the complete graph $K_v$ admitting an automorphism group G acting doubly transitively on the set of vertices. The vertex-set $V(K_v)$ can then be identified with the point-set of AG(n, p) and each 2-factor of F 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 AGL(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 / Buratti, Marco; Bonisoli, A.; Mazzuoccolo, G.. - In: JOURNAL OF COMBINATORIAL DESIGNS. - ISSN 1063-8539. - 15:(2007), pp. 120-132. [10.1002/jcd.20111]

Doubly transitive 2-factorizations

BURATTI, Marco;
2007

Abstract

Let F be a 2-factorization of the complete graph $K_v$ admitting an automorphism group G acting doubly transitively on the set of vertices. The vertex-set $V(K_v)$ can then be identified with the point-set of AG(n, p) and each 2-factor of F 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 AGL(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
graph; 2-factorization; doubly transitive permutation group; design
01 Pubblicazione su rivista::01a Articolo in rivista
Doubly transitive 2-factorizations / Buratti, Marco; Bonisoli, A.; Mazzuoccolo, G.. - In: JOURNAL OF COMBINATORIAL DESIGNS. - ISSN 1063-8539. - 15:(2007), pp. 120-132. [10.1002/jcd.20111]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1654647
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