TY - JOUR
T1 - Rigidity with few locations
AU - Adiprasito, Karim
AU - Nevo, Eran
N1 - Publisher Copyright:
© 2020, The Hebrew University of Jerusalem.
PY - 2020/10
Y1 - 2020/10
N2 - Graphs triangulating the 2-sphere are generically rigid in 3-space, due to Gluck-Dehn-Alexandrov-Cauchy. We show there is a finite subset A in 3-space so that the vertices of each graph G as above can be mapped into A to make the resulted embedding of G infinitesimally rigid. This assertion extends to the triangulations of any fixed compact connected surface, where the upper bound obtained on the size of A increases with the genus. The assertion fails, namely no such finite A exists, for the larger family of all graphs that are generically rigid in 3-space and even in the plane.
AB - Graphs triangulating the 2-sphere are generically rigid in 3-space, due to Gluck-Dehn-Alexandrov-Cauchy. We show there is a finite subset A in 3-space so that the vertices of each graph G as above can be mapped into A to make the resulted embedding of G infinitesimally rigid. This assertion extends to the triangulations of any fixed compact connected surface, where the upper bound obtained on the size of A increases with the genus. The assertion fails, namely no such finite A exists, for the larger family of all graphs that are generically rigid in 3-space and even in the plane.
UR - http://www.scopus.com/inward/record.url?scp=85094169593&partnerID=8YFLogxK
U2 - 10.1007/s11856-020-2076-y
DO - 10.1007/s11856-020-2076-y
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AN - SCOPUS:85094169593
SN - 0021-2172
VL - 240
SP - 711
EP - 723
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 2
ER -