On Edge Numberings of the n-Cube Graph

Given two disjoint groups U and V each containing 2n−1 people. Suppose an experiment (or a game) requires pairwise comparisons between u ∈ U and v ∈ V in such a way that u ∈ U (v ∈ V ) is compared exactly with n people v ∈ V (u ∈ U). Only one comparison can be done at a time, and the comparisons are made along the n2n−1 edges of the n−cube graph Qn with vertex classes U and V . The paper deals with sequential orderings of these n2n−1 pairs (u, v) ∈ U×V for which the maximum time duration a person has to stay in the sequence for comparison purposes or the total time duration of the 2n people in the sequence, respectively, is small. Analogous problem of finding optimal sequences of all k−subsets of an n−set or of all pairs (x, y) ∈ X×Y , |X| = |Y | = n, were considered in [7] and [3] respectively.