A 2-factorization of a simple graph $Gamma$ is called 2-pyramidal if it admits an automorphism group G fixing two vertices and acting sharply transitively on the others. Here we show that such a 2-factorization may exist only if $Gamma$ is a cocktail party graph, i.e., $Gamma = K_{2n} − I$ with I being a 1-factor. It will be said of the first or second type according to whether the involutions of G form a unique conjugacy class or not. As far as we are aware, 2-factorizations of the second type are completely new. We will prove, in particular, that $K_{2n} − I$ admits a 2-pyramidal 2-factorization of the second type if and only if n ≡ 1 (mod 8).

The structure of 2-pyramidal 2-factorizations / Buratti, Marco; Traetta, Tommaso. - In: GRAPHS AND COMBINATORICS. - ISSN 0911-0119. - 31:3(2015), pp. 523-535. [10.1007/s00373-014-1408-2]

The structure of 2-pyramidal 2-factorizations

BURATTI, Marco;
2015

Abstract

A 2-factorization of a simple graph $Gamma$ is called 2-pyramidal if it admits an automorphism group G fixing two vertices and acting sharply transitively on the others. Here we show that such a 2-factorization may exist only if $Gamma$ is a cocktail party graph, i.e., $Gamma = K_{2n} − I$ with I being a 1-factor. It will be said of the first or second type according to whether the involutions of G form a unique conjugacy class or not. As far as we are aware, 2-factorizations of the second type are completely new. We will prove, in particular, that $K_{2n} − I$ admits a 2-pyramidal 2-factorization of the second type if and only if n ≡ 1 (mod 8).
2015
1-Rotational 2-Factorization; 2-Pyramidal 2-Factorization; Conjugacy; Group action
01 Pubblicazione su rivista::01a Articolo in rivista
The structure of 2-pyramidal 2-factorizations / Buratti, Marco; Traetta, Tommaso. - In: GRAPHS AND COMBINATORICS. - ISSN 0911-0119. - 31:3(2015), pp. 523-535. [10.1007/s00373-014-1408-2]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1654632
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