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 × 2n−1 mesh can be embedded into TNn with dilation 1 and expansion 1. (2) For any integer n ⩾ 4, an m × k(m ⩾ 3, k ⩾ 3) mesh cannot be embedded into TNn with dilation 1. (3) For any integer n ⩾ 4, two node-disjoint 4 × 2n−3 meshes can be embedded into TNn with dilation 2 and expansion 1.