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Doubly transitive 2-factorizations

✍ Scribed by Arrigo Bonisoli; Marco Buratti; Giuseppe Mazzuoccolo

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
142 KB
Volume
15
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

Let $\cal F$ 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 $\cal F$ 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 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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