Free Edge Lengths in Plane Graphs
Zachary Abel, Robert Connelly, Sarah Eisenstat, Radoslav Fulek, Filip Morić, Yoshio Okamoto, Tibor Szabó, Csaba D. Tóth · 2014
We study the impact of metric constraints on the realizability of planar graphs. Let G be a subgraph of a planar graph H (where H is the "host" of G). The graph G is free in H if for every choice of positive lengths for the edges of G, the host H has a planar straight-line embedding that realizes these lengths; and G is extrinsically free in H if all constraints on the edge lengths of G depend on G only, irrespective of additional edges of the host H.