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A generalization of the Oberwolfach problem and C t ‐factorizations of complete equipartite graphs
Author(s) -
Liu Jiuqiang
Publication year - 2000
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(2000)8:1<42::aid-jcd6>3.0.co;2-r
Subject(s) - generalization , combinatorics , mathematics , delegation , discrete mathematics , arithmetic , management , mathematical analysis , economics
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 ${T}_{1},{T}_{2},\ldots,{T}_{s}$ (where $T_i$ can accommodate $t_i \ge 3$ people and $\sum t_i=mn$ ) for k different meals so that each person has every other person not in the same delegation for a neighbour exactly once?”. We will concentrate on the case when all tables accommodate the same number t of people, give a complete solution for t even and settle most cases for t odd. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 42–49, 2000