Morphing Planar Graphs While Preserving Edge Directions
Biedl, Therese and Lubiw, Anna and Spriggs, Michael (2006) Morphing Planar Graphs While Preserving Edge Directions. In: Graph Drawing 13th International Symposium, GD 2005, September 12-14, 2005, Limerick, Ireland , pp. 13-24 (Official URL: http://dx.doi.org/10.1007/11618058_2).
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Two straight-line drawings P,Q of a graph (V,E) are called parallel if, for every edge (u,v) in E, the vector from u to v has the same direction in both P and Q. We study problems of the form: given simple, parallel drawings P,Q does there exist a continuous transformation between them such that intermediate drawings of the transformation remain simple and parallel with P (and Q)? We prove that a transformation can always be found in the case of orthogonal drawings; however, when edges are allowed to be in one of three or more slopes the problem becomes NP-hard.
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