We consider one–factorizations of complete graphs which possess an automorphism group fixing k ≥ 0 vertices and acting regularly (i.e., sharply transitively) on the others. Since the cases k = 0 and k = 1 are well known in literature, we study the case k>=2 in some detail. We prove that both k and the order of the group are even and the group necessarily contains k − 1 involutions. Constructions for some classes of groups are given. In particular we extend the result of [7]: let G be an abelian group of even order and with k − 1 involutions, a one–factorization of a complete graph admitting G as an automorphism group fixing k vertices and acting regularly on the others can be constructed.

k–Pyramidal One–Factorizations / Mazzuoccolo, Giuseppe; Rinaldi, Gloria. - In: GRAPHS AND COMBINATORICS. - ISSN 0911-0119. - STAMPA. - 23:3(2007), pp. 315-326. [10.1007/s00373-007-0734-z]

k–Pyramidal One–Factorizations

MAZZUOCCOLO, Giuseppe;RINALDI, Gloria
2007

Abstract

We consider one–factorizations of complete graphs which possess an automorphism group fixing k ≥ 0 vertices and acting regularly (i.e., sharply transitively) on the others. Since the cases k = 0 and k = 1 are well known in literature, we study the case k>=2 in some detail. We prove that both k and the order of the group are even and the group necessarily contains k − 1 involutions. Constructions for some classes of groups are given. In particular we extend the result of [7]: let G be an abelian group of even order and with k − 1 involutions, a one–factorization of a complete graph admitting G as an automorphism group fixing k vertices and acting regularly on the others can be constructed.
2007
23
3
315
326
k–Pyramidal One–Factorizations / Mazzuoccolo, Giuseppe; Rinaldi, Gloria. - In: GRAPHS AND COMBINATORICS. - ISSN 0911-0119. - STAMPA. - 23:3(2007), pp. 315-326. [10.1007/s00373-007-0734-z]
Mazzuoccolo, Giuseppe; Rinaldi, Gloria
File in questo prodotto:
File Dimensione Formato  
k_pyr_postprint.pdf

Open access

Descrizione: Articolo principale
Tipologia: Versione dell'autore revisionata e accettata per la pubblicazione
Dimensione 4.65 MB
Formato Adobe PDF
4.65 MB Adobe PDF Visualizza/Apri
KpyrOneFact2007.pdf

Accesso riservato

Tipologia: Versione pubblicata dall'editore
Dimensione 130.5 kB
Formato Adobe PDF
130.5 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/613662
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 5
social impact