Realizability of Graphs

@article{Belk2007RealizabilityOG,
  title={Realizability of Graphs},
  author={Maria Belk and Robert Connelly},
  journal={Discrete & Computational Geometry},
  year={2007},
  volume={37},
  pages={125-137}
}
A graph is d-realizable if, for every configuration of its vertices in E N , there exists a another corresponding configuration in Ed with the same edge lengths. A graph is 2-realizable if and only if it is a partial 2-tree, i.e., a subgraph of the 2-sum of triangles in the sense of graph theory. We show that a graph is 3-realizable if and only if it does not have K5 or the 1-skeleton of the octahedron as a minor. 

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