Parallel morphing of trees and cycles.
Thérèse Biedl, Anna Lubiw, Michael J. Spriggs · 2003
We prove that for any two simple chains [more generally, trees] in R d 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.