... solved in his thesis the circular arrangement problem for the hypercube, and Bezrukov and Schroeder [1], who showed that for trees the solutionsfor the linear arrangement problem and the circular ... from one of u and v, and at distance atleast j from the other one. Therefore, for any i ∈ V ,andanyuv ∈ Ei,j\ Ei,j−1,wehaveloadu,v(i)=∆f(j), according to the definition of the load. Let ... k)).Theorem 11. For every >0 and k ≤ n1−,asn →∞, we haveν1(G(n, k))=Θ(k4n2log n). (44)Proof. The upper bound follows from Theorem 1. The lower bound follows from Theo-rem 2 and the...