Hamiltonian paths and cycles with prescribed edges in the 3-ary n-cube
The k-ary n-cube has been one of the most popular interconnection networks for massively parallel systems. Given a set P of at most 2n - 2 (n >= 2) prescribed edges and two vertices u and v, we show that the 3-ary n-cube contains a Hamiltonian path between u and v passing through all edges of P if and only if the subgraph induced by P consists of pairwise vertex-disjoint paths, none of them having u or v as internal vertices or both of them as end-vertices. As an immediate result, the 3-ary n-cube contains a Hamiltonian cycle passing through a set P of at most 2n - 1 prescribed edges if and only lithe subgraph induced by P consists of pairwise vertex-disjoint paths. (C) 2011 Elsevier Inc. All rights reserved.
hamiltonian paths prescribed edges 3-ary n-cubes hamiltonian cycles