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2011 | 9 | 5 | 1114-1120
Tytuł artykułu

Rectangular table negotiation problem revisited

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We solve the last missing case of a “two delegation negotiation” version of the Oberwolfach problem, which can be stated as follows. Suppose we have two negotiating delegations with n=mk members each and we have a seating arrangement such that every day the negotiators sit at m tables with k people of the same delegation at one side of each table. Every person can effectively communicate just with three nearest persons across the table. Our goal is to guarantee that over the course of several days, every member of each delegation can communicate with every member of the other delegation exactly once. We denote by H(k, 3) the graph describing the communication at one table and by mH(k, 3) the graph consisting of m disjoint copies of H(k, 3). We completely characterize all complete bipartite graphs K n,n that can be factorized into factors isomorphic to G =mH(k, 3) for k ≡ 2 (mod 4) by showing that the necessary conditions n=mk and m ≡ 0 mod(3k−2)/4 are also sufficient. This results complement previous characterizations for k ≡ 0, 1, 3 (mod 4) to settle the problem in full.
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
5
Strony
1114-1120
Opis fizyczny
Daty
wydano
2011-10-01
online
2011-07-26
Twórcy
Bibliografia
  • [1] Colbourn C.J., Dinitz J.H. (Eds.), The CRC Handbook of Combinatorial Designs, CRC Press Ser. Discrete Math. Appl., CRC Press, Boca Raton, 1996
  • [2] Chitra V., Muthusamy A., Bipartite variation of the cheesecake factory problem (in preparation)
  • [3] El-Zanati S.I., Vanden Eynden C., On Rosa-type labelings and cyclic graph decompositions, Math. Slovaca, 2009, 59(1), 1–18 http://dx.doi.org/10.2478/s12175-008-0108-x
  • [4] Froncek D., Oberwolfach rectangular table negotiation problem, Discrete Math., 2009, 309(2), 501–504 http://dx.doi.org/10.1016/j.disc.2008.02.034
  • [5] Piotrowski W.-L., The solution of the bipartite analogue of the Oberwolfach problem, Discrete Math., 97(1–3), 1991, 339–356 http://dx.doi.org/10.1016/0012-365X(91)90449-C
  • [6] Ringel G., Lladó A.S., Serra O., Decomposition of complete bipartite graphs into trees, DMAT Research Report, Univ. Politecnica de Catalunya, 1996, #11
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0064-5
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