Oberwolfach rectangular table negotiation problem

We completely solve certain case of a “two delegation negotiation” version of the Oberwolfach problem, which can be stated as follows. Let H(k, 3) be a bipartite graph with bipartition X = {x1, x2, . . . , xk}, Y = {y1, y2, . . . , yk} and edges x1 y1, x1 y2, xk yk−1, xk yk , and xi yi−1, xi yi , xi yi+1 for i = 2, 3, . . . , k − 1. We completely characterize all complete bipartite graphs Kn,n that can be factorized into factors isomorphic to G = m H(k, 3), where k is odd and m H(k, 3) is the graph consisting of m disjoint copies of H(k, 3). c © 2008 Elsevier B.V. All rights reserved.