On \(\lambda\)-fold equipartite Oberwolfach problem with uniform table sizes
The following generalization of the classical Oberwolfach problem is considered: At a gathering there are \(n\) delegations with \(m\) people each. Is it possible to arrange a seating of \(nm\) people at \(s\) round tables where each table can accommodate \(t\) people (\(st=nm\)) for \(k\) different occasions such that each person has every other person not in the same delegation for a neighbor exactly \(\lambda\) times? It is proved that for \(t\geq 3,n\geq 2,\lambda\geq 2\) the solution exists precisely when \(t| mn\), \(\lambda m(n-1)\) is even, \(t\) is even when \(n=2\) and \((m,n,t,\lambda )\notin \{ (2,3,3,2j+1),(1,6,3,4j+2)\mid j\geq 0\}\). For \(\lambda =1\) the problem was solved in [\textit{J. Liu}, J. Comb. Theory, Ser. A 101, No. 1, 20--34 (2003; Zbl 1015.05074)].
scientific article; zbMATH DE number 2067284