On the generalized honeymoon Oberwolfach problem

Masoomeh Akbari, University of Ottawa

The Honeymoon Oberwolfach Problem (HOP), introduced by Šajna, is a recent variant of the classic Oberwolfach Problem. This problem asks whether it is possible to seat 2m1 + 2m2 + · · · + 2mt = 2n participants, consisting of n newlywed couples, at t round tables of sizes 2m1, 2m2, . . . , 2mt for 2n − 2 nights, so that each participant sits next to their spouse every night and next to every other participant exactly once. This problem is denoted by HOP(2m1, 2m2, . . . , 2mt). Jerade, Lepine, and Sajna have studied the HOP and resolved several important cases.

We generalized the HOP by allowing tables of size two, relaxing the previous restriction that tables must have a minimum size of four. In the generalized HOP, we aim to seat the 2n participants at s tables of size 2 and t round tables of sizes 2m1, 2m2, . . . , 2mt, where 2n = 2s + 2m1 + 2m2 + · · · + 2mt and mi ≥ 2, while preserving the adjacency conditions of the HOP. We denote this problem by HOP(2⟨s⟩, 2m1, . . . , 2mt).

In this talk, we will present a general approach to this problem, as well as recent solutions to several cases.