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Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Rigid cylindrical frameworks with two coincident points
AU - Jackson, Bill
AU - Kaszanitzky, Viktoria
AU - Nixon, Anthony Keith
PY - 2019/1
Y1 - 2019/1
N2 - 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.
AB - 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.
KW - Infinitesimal rigidity
KW - Framework on a surface
KW - Count matroid
KW - Deletion/contraction characterisation
KW - Coincident points
U2 - 10.1007/s00373-018-1983-8
DO - 10.1007/s00373-018-1983-8
M3 - Journal article
VL - 35
SP - 141
EP - 168
JO - Graphs and Combinatorics
JF - Graphs and Combinatorics
SN - 0911-0119
IS - 1
ER -