The Honeymoon Oberwolfach Problem: small cases

The Honeymoon Oberwolfach Problem HOP(2m₁,2m₂,…,2mₜ) asks the following question. Given n=m₁+m₂+… +mₜ newlywed couples at a conference and t round tables of sizes 2m₁,2m₂,…,2mₜ, is it possible to arrange the $2n$ participants at these tables for $2n-2$ meals so that each participant sits next to their spouse at every meal, and sits next to every other participant exactly once? A solution to HOP(2m₁,2m₂,…,2mₜ) is a decomposition of K₂ₙ+(2n-3)I, the complete graph K₂ₙ with $2n-3$ additional copies of a fixed 1-factor I, into 2-factors, each consisting of disjoint I-alternating cycles of lengths 2m₁,2m₂,…,2mₜ. The Honeymoon Oberwolfach Problem was introduced in a 2019 paper by Lepine and {S}ajna. The authors conjectured that HOP(2m₁,2m₂,…, 2mₜ) has a solution whenever the obvious necessary conditions are satisfied, and proved the conjecture for several large cases, including the uniform cycle length case m₁=…=mₜ, and the small cases with n ≤ 9. In the present paper, we extend the latter result to all cases with n ≤ 20 using a computer search.