On the existence of paradoxical motions of generically rigid graphs on the sphere

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F21%3A00350288" target="_blank" >RIV/68407700:21240/21:00350288 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1137/19M1289467" target="_blank" >https://doi.org/10.1137/19M1289467</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/19M1289467" target="_blank" >10.1137/19M1289467</a>

Result language
angličtina
Original language name
On the existence of paradoxical motions of generically rigid graphs on the sphere
Original language description
We interpret realizations of a graph on the sphere up to rotations as elements of a moduli space of curves of genus zero. We focus on those graphs that admit an assignment of edge lengths on the sphere resulting in a flexible object. Our interpretation of realizations allows us to provide a combinatorial characterization of these graphs in terms of the existence of particular colorings of the edges. Moreover, we determine necessary relations for flexibility between the spherical lengths of the edges. We conclude by classifying all possible motions on the sphere of the complete bipartite graph with 3+3 vertices where no two vertices coincide or are antipodal.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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