Flexibility and rigidity of frameworks consisting of triangles and parallelograms

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Flexibility and rigidity of frameworks consisting of triangles and parallelograms

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Flexibility and rigidity of frameworks consisting of triangles and parallelograms

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF22-04381L" target="_blank" >GF22-04381L: Paradoxně pohyblivé realizace grafů</a><br>

Návaznosti

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

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Computational Geometry: Theory and Applications

ISSN

0925-7721

e-ISSN

1879-081X

Svazek periodika

120

Číslo periodika v rámci svazku

June

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

23

Strana od-do

—

Kód UT WoS článku

001200483600001

EID výsledku v databázi Scopus

2-s2.0-85185536089