Rectangular table negotiation problem revisited

• Autorzy: Dalibor Froncek , Michael Kubesa
• 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.

Słowa kluczowe

EN

Oberwolfach problem; Graph decomposition; Graph factorization

Kategorie tematyczne

• 05C70: Factorization, matching, partitioning, covering and packing
• 05C78: Graph labelling (graceful graphs, bandwidth, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 5
• Strony: 1114-1120

Daty

wydano

2011-10-01

online

2011-07-26

Twórcy

autor

Dalibor Froncek

• University of Minnesota Duluth

autor

Michael Kubesa

• Technical University Ostrava

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

Identyfikatory

DOI

10.2478/s11533-011-0064-5