Bracing frameworks consisting of parallelograms

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Bracing frameworks consisting of parallelograms

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Bracing frameworks consisting of parallelograms

Popis výsledku anglicky

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.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Centrum pokročilých aplikovaných přírodních věd</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

The Art of Discrete and Applied Mathematics

ISSN

2590-9770

e-ISSN

2590-9770

Svazek periodika

5

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

SI - Slovinská republika

Počet stran výsledku

21

Strana od-do

1-21

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85117793129