Bipanconnectivity and Bipancyclicity in k-ary n-cubes

In this paper, we give precise solutions to problems posed by Wang et al. and by Hsieh et al. In particular, we show that Qkn is bipanconnected and edge-bipancyclic, when k >= 3 and n >= 2, and we also show that when k is odd, Q(n)(k) is m-panconnected, for m = n(k-1)+2k-6/2 and (k-1) pancyclic (these bounds are optimal). We introduce a path-shortening technique, called progressive shortening, and strengthen existing results, showing that when paths are formed using progressive shortening, then these paths can be efficiently constructed and used to solve a problem relating to the distributed simulation of linear arrays and cycles in a parallel machine whose interconnection network is Q(n)(k), even in the presence of a faulty processor.