Flexibility and rigidity of frameworks consisting of triangles and parallelograms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F24%3A00373180" target="_blank" >RIV/68407700:21240/24:00373180 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.comgeo.2023.102055" target="_blank" >https://doi.org/10.1016/j.comgeo.2023.102055</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.comgeo.2023.102055" target="_blank" >10.1016/j.comgeo.2023.102055</a>

Result language
angličtina
Original language name
Flexibility and rigidity of frameworks consisting of triangles and parallelograms
Original language description
A framework, which is a (possibly infinite) graph with a realization of its vertices in the plane, is called flexible if it can be continuously deformed while preserving the edge lengths. We focus on flexibility of frameworks in which 4-cycles form parallelograms. For the class of frameworks considered in this paper (allowing triangles), we prove that the following are equivalent: flexibility, infinitesimal flexibility, the existence of at least two classes of an equivalence relation based on 3- and 4-cycles and being a non -trivial subgraph of the Cartesian product of graphs. We study the algorithmic aspects and the rotationally symmetric version of the problem. The results are illustrated on frameworks obtained from tessellations by regular polygons.
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF22-04381L" target="_blank" >GF22-04381L: Paradoxical flexibility of frameworks</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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