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. - 32:9(2024), pp. 532-545. [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
32
9
532
545
The Oberwolfach Problem with loving couples / Rinaldi, Gloria. - In: JOURNAL OF COMBINATORIAL DESIGNS. - ISSN 1063-8539. - 32:9(2024), pp. 532-545. [10.1002/jcd.21946]
Rinaldi, Gloria
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1339306
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