We generalize the well-known Oberwolfach problem posed by Ringel in 1967. We suppose to have v/2 couples (here v is an even integer) and suppose that they have to be seated for several nights at t round tables in such a way that each person seats next to his partner exactly r >=0 times and next to every other person exactly once. We call this problem the Oberwolfach problem with loving couples. When r=0, the problem coincides with the so-called spouse-avoiding variant, which was introduced by Huang, Kotzig, and Rosa in 1979. While if either r=2 or requals the number of nights, it corresponds to the spouse-loving variant or to the Honeymoon variant, which was recently studied by Bolohan et al. and by Lepine and Sajna, respectively. In this paper, for each possible choice of r, we construct many classes of solutions to the Oberwolfach problem with loving couples. We also obtain new solutions to the Honeymoon variant.

The Oberwolfach Problem with loving couples / Rinaldi, Gloria. - In: JOURNAL OF COMBINATORIAL DESIGNS. - ISSN 1063-8539. - (2024), pp. 1-14. [10.1002/jcd.21946]

The Oberwolfach Problem with loving couples

Gloria Rinaldi
2024

Abstract

We generalize the well-known Oberwolfach problem posed by Ringel in 1967. We suppose to have v/2 couples (here v is an even integer) and suppose that they have to be seated for several nights at t round tables in such a way that each person seats next to his partner exactly r >=0 times and next to every other person exactly once. We call this problem the Oberwolfach problem with loving couples. When r=0, the problem coincides with the so-called spouse-avoiding variant, which was introduced by Huang, Kotzig, and Rosa in 1979. While if either r=2 or requals the number of nights, it corresponds to the spouse-loving variant or to the Honeymoon variant, which was recently studied by Bolohan et al. and by Lepine and Sajna, respectively. In this paper, for each possible choice of r, we construct many classes of solutions to the Oberwolfach problem with loving couples. We also obtain new solutions to the Honeymoon variant.
2024
20-mag-2024
1
14
The Oberwolfach Problem with loving couples / Rinaldi, Gloria. - In: JOURNAL OF COMBINATORIAL DESIGNS. - ISSN 1063-8539. - (2024), pp. 1-14. [10.1002/jcd.21946]
Rinaldi, Gloria
File in questo prodotto:
File Dimensione Formato  
JCD pubblicato.pdf

Accesso riservato

Descrizione: articolo completo
Tipologia: Versione pubblicata dall'editore
Dimensione 553.94 kB
Formato Adobe PDF
553.94 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/11380/1339306
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact