Realizability of Graphs |
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Authors: | Maria Belk Robert Connelly |
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Institution: | (1) Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA;(2) Department of Mathematics, Cornell University, Ithaca, NY 14853-4201, USA |
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Abstract: | A graph is d-realizable if, for every configuration of its vertices in EN, 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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