Parallel morphing of trees and cycles

We prove that for any two simple chains [more generally, trees] in Rd with corresponding edges parallel, there is a parallel morph between them—i.e. a morph in which all intermediate chains [trees] remain simple and parallel to the original. A similar result had been proved by Guibas et al. [8] for simple cycles in R2 . We prove that the result for cycles does not extend to R3 by giving two simple cycles, with corresponding edges parallel, that represent the same knot, and yet have no parallel morph.

• Type: Conference
• Year: 2003
• Where: CCCG
• Authors: Therese C. Biedl, Anna Lubiw, Michael J. Spriggs
• Keywords: CCCG 2003, CCCG 2007, Intermediate Chains, Parallel Morph, Simple Chains