Let Formula: see text be the Cartesian product of Formula: see text paths, with at least one path having an even number of vertices. Let Formula: see text and Formula: see text be integers satisfying Formula: see text and Formula: see text, and let Formula: see text be a set of Formula: see text vertices of Formula: see text. We prove that there exists an Formula: see text-factor Formula: see text of Formula: see text consisting of Formula: see text components Formula: see text, where each component Formula: see text is an Formula: see text-regular, Formula: see text-connected, bipancyclic graph containing exactly one vertex of Formula: see text. Thus, an Formula: see text-dimensional grid of even order can be partitioned into regular, connected and bipancyclic subnetworks passing through prescribed vertices. This extends related results for tori and, as a corollary, also applies to hypercubes.
Badadhe et al. (Thu,) studied this question.