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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
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
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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