This work on the fold-and-cut problem has been generalized to arbitrary plane graphs; see my fold-and-cut webpage for links to related papers.
Further updates concerning this technical report:
- In joint work with Therese Biedl, Martin Demaine, Sylvain Lazard, Anna Lubiw, Joseph O'Rourke, Steve Robbins, Ileana Streinu, Godfried Toussaint, and Sue Whitesides, it has been shown that general trees linkages cannot always be straightened (disallowing extra folds); see the CCCG'98 paper. This solves the open problem mentioned in Section 5.3, but does not disprove the closed-chain conjecture as claimed in this technical report. In fact, the closed-chain conjecture is true; see my linkage webpage.
- In joint work with Marshall Bern, David Eppstein, and Barry Hayes, the first part of Conjecture 1 has been disproved: it is possible to combine several "local" bisector graphs (instead of using one "global" one) to solve the folding-and-cutting problem. See the FUN'98 paper.