Hamiltonian Paths and Cycles Passing through Prescribed Edges in the Balanced Hypercubes

Authors: Dongqin Cheng

Abstract:

The n-dimensional balanced hypercube BHn (n ≥ 1) has been proved to be a bipartite graph. Let P be a set of edges whose induced subgraph consists of pairwise vertex-disjoint paths. For any two vertices u, v from different partite sets of V (BHn). In this paper, we prove that if |P| ≤ 2n − 2 and the subgraph induced by P has neither u nor v as internal vertices, or both of u and v as end-vertices, then BHn contains a Hamiltonian path joining u and v passing through P. As a corollary, if |P| ≤ 2n−1, then the BHn contains a Hamiltonian cycle passing through P.

Keywords: interconnection network, balanced hypercube, Hamiltonian cycle, prescribed edges