Upward Planar Morphs - Da Lozzo, Giordano; Di Battista, Giuseppe; Frati, Fabrizio; Patrignani, Maurizio; Roselli, Vincenzo (Algorithmica, 2020)
We prove that, given two topologically-equivalent upward planar straight-line drawings of an n -vertex directed graph G , there always exists a morph between them such that all the intermediate drawings of the morph are upward planar and straight-line. Such a morph consists of O (1) morphing steps if G is a reduced planar st -graph, O ( n ) morphing steps if G is a planar st -graph, O ( n ) morphing steps if G is a reduced upward planar graph, and O ( n 2 ) morphing steps if G is a general upward planar graph. Further, we show that Ω ( n ) morphing steps might be necessary for an upward planar morph between two topologically-equivalent upward planar straight-line drawings of an n -vertex path.