TY - JOUR

T1 - Rectangular table negotiation problem revisited

AU - Froncek, Dalibor

AU - Kubesa, Michael

PY - 2011/10

Y1 - 2011/10

N2 - 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 Kn,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.

AB - 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 Kn,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.

KW - Graph decomposition

KW - Graph factorization

KW - Oberwolfach problem

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U2 - 10.2478/s11533-011-0064-5

DO - 10.2478/s11533-011-0064-5

M3 - Article

AN - SCOPUS:79960723649

SN - 1895-1074

VL - 9

SP - 1114

EP - 1120

JO - Central European Journal of Mathematics

JF - Central European Journal of Mathematics

IS - 5

ER -