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One of the key problems in parallel processing is finding disjoint paths in the underlying graph of an interconnection network. The  disjoint path cover  of a graph is a set of pairwise vertex-disjoint paths that altogether cover every vertex of the graph. Given disjoint source and sink sets,  S  = &#x007B; s  1 ,...,  s k  &#x007D; and  T  = &#x007B; t  1 ,...,  t k  &#x007D;, in graph  G , an  unpaired many-to-many k-disjoint path cover  joining  S  and  T  is a disjoint path cover &#x007B; P  1 ,...,  P k  &#x007D;, in which each path  P i   runs from source  s i   to some sink  t j  . In this paper, we reveal that a nonbipartite torus-like graph, if built from lower dimensional torus-like graphs that have good disjoint-path-cover properties of the unpaired type, retains such a good property. As a result, an  m -dimensional nonbipartite torus,  m  &#x2265; 2, with at most  f  vertex and/or edge faults has an unpaired many-to-many  k -disjoint path cover joining arbitrary disjoint sets  S  and  T  of size  k  each, subject to  k  &#x2265; 2 and  f  +  k  &#x2264; 2 m  &#x2013; 2. The bound of 2 m  &#x2013; 2 on  f  +  k  is nearly optimal.

Unpaired Many-to-Many Disjoint Path Covers in Nonbipartite Torus-Like Graphs with Faulty Elements