Bracing frameworks consisting of parallelograms
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F22%3A00358943" target="_blank" >RIV/68407700:21240/22:00358943 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.26493/2590-9770.1379.7a4" target="_blank" >https://doi.org/10.26493/2590-9770.1379.7a4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.26493/2590-9770.1379.7a4" target="_blank" >10.26493/2590-9770.1379.7a4</a>
Alternative languages
Result language
angličtina
Original language name
Bracing frameworks consisting of parallelograms
Original language description
A rectangle in the plane can be continuously deformed preserving its edge lengths, but adding a diagonal brace prevents such a deformation. Bolker and Crapo characterized combinatorially which choices of braces make a grid of squares infinitesimally rigid using a bracing graph: a bipartite graph whose vertices are the columns and rows of the grid, and a row and column are adjacent if and only if they meet at a braced square. Duarte and Francis generalized the notion of the bracing graph to rhombic carpets, proved that the connectivity of the bracing graph implies rigidity and stated the other implication without proof. Nagy Kem gives the equivalence in the infinitesimal setting. We consider continuous deformations of braced frameworks consisting of a graph from a more general class and its placement in the plane such that every 4-cycle forms a parallelogram. We show that rigidity of such a braced framework is equivalent to the non-existence of a special edge coloring, which is in turn equivalent to the corresponding bracing graph being connected.
Czech name
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Czech description
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Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
The Art of Discrete and Applied Mathematics
ISSN
2590-9770
e-ISSN
2590-9770
Volume of the periodical
5
Issue of the periodical within the volume
2
Country of publishing house
SI - SLOVENIA
Number of pages
21
Pages from-to
1-21
UT code for WoS article
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EID of the result in the Scopus database
2-s2.0-85117793129