Embedding Hamiltonian Paths with Prescribed Linear Forests into k-ary n-Cube Networks

Graph embedding is a fundamental problem in computer science. Let [Formula: see text] (resp., [Formula: see text]) be the interconnection network for a parallel computer system [Formula: see text] (resp., [Formula: see text]). If [Formula: see text] could be embedded into [Formula: see text], then [Formula: see text] can simulate [Formula: see text]’s behavior. The [Formula: see text]-ary [Formula: see text]-cube [Formula: see text] is a node-symmetric and link-symmetric recursive interconnection network for parallel computer systems. Let [Formula: see text] be a prescribed linear forest of [Formula: see text], and let [Formula: see text] and [Formula: see text] be any two distinct nodes in [Formula: see text] such that [Formula: see text] has no path with [Formula: see text] or [Formula: see text] as internal nodes, or both as end-nodes. This paper shows that there is a Hamiltonian path passing through [Formula: see text] between [Formula: see text] and [Formula: see text] in [Formula: see text] with [Formula: see text] and odd [Formula: see text] even if the number of links in [Formula: see text] is up to [Formula: see text].