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On -Fold Equipartite Oberwolfach Problem with Uniform Table Sizes
Jiuqiang Liu1,2 and Don R. Lick1
1Eastern Michigan University,Ypsilanti, MI 48197, USA
jliu@emich.edu
2Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, P.R. China
Annals of Combinatorics 7 (3) p.315-323 September, 2003
AMS Subject Classification: 05B05
Abstract:
We consider the following generalization of the Oberwolfach problem: "At a gathering there are n delegations each having m people. Is it possible to arrange a seating of mn people present at s round tables T1, T2, ..., Ts (where each Ti can accommodate ti3 people and ti = mn) for k different meals so that each person has every other person not in the same delegation for a neighbor exactly times?" For = 1, Liu has obtained the complete solution to the problem when all tables accommodate the same number t of people. In this paper, we give the complete solution to the problem for 2 when all tables have uniform sizes t.
Keywords: resolvable cycle design, Hamiltonian decomposition, cycle frame, cycle factorization

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