Embedding meshes into twisted-cubes

The n-dimensional twisted-cube, TNn, is a variation of the hypercube. In this paper, we study embedding of meshes into TNn. We prove three major results in this paper: (1) For any integer n >= 1, a 2 x 2(n-1) mesh can be embedded into TNn with dilation 1 and expansion 1. (2) For any integer n >= 4, an m x k(m >= 3, k >= 3) mesh cannot be embedded into TNn with dilation 1. (3) For any integer n >= 4, two node-disjoint 4 x 2(n-3) meshes can be embedded into TNn with dilation 2 and expansion 1. (C) 2011 Elsevier Inc. All rights reserved.