A solution to the three disjoint path problem on honeycomb tori

In a previous paper we solved an open problem named as the three disjoint path problem on honeycomb meshes. In this paper we extend the technique used to solve the related problem on honeycomb tori. The result gives the minimum possible length of the longest of any three disjoint paths between two given nodes in a torus. The problem has practical benefits in the fault tolerant aspects of interconnection topologies.