Unfolding Orthotubes with a Dual Hamiltonian Path

Abstract

An orthotube consists of orthogonal boxes (e.g., unit cubes) glued face-to-face to form a path. In 1998, Biedl et al. showed that every orthotube has a grid unfolding : a cutting along edges of the boxes so that the surface unfolds into a connected planar shape without overlap. We give a new algorithmic grid unfolding of orthotubes with the additional property that the rectangular faces are attached in a single path -a Hamiltonian path on the rectangular faces of the orthotube surface.