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- W1528971596 abstract "We show that planar embeddable 3-connected CAD graphs are generically non-soluble. A CAD graph represents a configuration of points on the Euclidean plane with just enough distance dimensions between them to ensure rigidity. Formally, a CAD graph is a maximally independent graph, that is, one that satisfies the vertex-edge count 2v - 3 = e together with a corresponding inequality for each subgraph. The following main theorem of the paper resolves a conjecture of Owen in the planar case. Let G be a maximally independent 3-connected planar graph, with more than 3 vertices, together with a realisable assignment of generic dimensions for the edges which includes a normalised unit length (base) edge. Then, for any solution configuration for these dimensions on a plane, with the base edge vertices placed at rational points, not all coordinates of the vertices lie in a radical extension of the dimension field." @default.
- W1528971596 created "2016-06-24" @default.
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- W1528971596 date "2003-11-04" @default.
- W1528971596 modified "2023-09-27" @default.
- W1528971596 title "Generic 3-connected planar constraint systems are not soluble by radicals" @default.
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