Graph flattenability

Summary

Flattenability in some $d$-dimensional normed vector space is a property of graphs which states that any embedding, or drawing, of the graph in some high dimension $d'$ can be "flattened" down to live in $d$-dimensions, such that the distances between pairs of points connected by edges are preserved. A graph $G$ is $d$-flattenable if every distance constraint system (DCS) with $G$ as its constraint graph has a $d$-dimensional framework. Flattenability was first called realizability, but the name was changed to avoid confusion with a graph having some DCS with a $d$-dimensional framework.