Rigid cylindrical frameworks with two coincident points

Jackson, Bill and Kaszanitzky, Viktoria and Nixon, Anthony Keith (2019) Rigid cylindrical frameworks with two coincident points. Graphs and Combinatorics, 35 (1). pp. 141-168. ISSN 0911-0119

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Abstract

We develop a rigidity theory for graphs whose vertices are constrained to lie on a cylinder and in which two given vertices are coincident. We apply our result to show that the vertex splitting operation preserves the global rigidity of generic frameworks on the cylinder, whenever it satisfies the necessary condition that the deletion of the edge joining the split vertices preserves generic rigidity.