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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.