Visibility-preserving convexifications using single-vertex moves
  Devadoss asked: (1) can every polygon be convexified so that no internal visibility (between vertices) is lost in the process? Moreover, (2) does such a convexification exist, in which exactly one vertex is moved at a time (that is, using {\em single-vertex moves})? We prove the redundancy of the "single-vertex moves" condition: an affirmative answer to (1) implies an affirmative answer to (2). Since Aichholzer et al. recently proved (1), this settles (2). 
Bernardo M. Abrego, Mario Cetina, Jesus Leanos, Gelasio Salazar
cs.CG cs.RO math.CO