Paradoxní pohyblivost: realizace grafů a mnohostěny

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F24%3A00380324" target="_blank" >RIV/68407700:21240/24:00380324 - isvavai.cz</a>

Výsledek na webu

<a href="https://csgg2024.zcu.cz/komplet.pdf" target="_blank" >https://csgg2024.zcu.cz/komplet.pdf</a>

DOI - Digital Object Identifier

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Jazyk výsledku

čeština

Název v původním jazyce

Paradoxní pohyblivost: realizace grafů a mnohostěny

Popis výsledku v původním jazyce

One of the main questions of rigidity theory is whether a bar-joint framework, which is a graph with a realization of its vertices in the d-dimensional space, allows a continuous deformation preserving the distances between adjacent vertices. If yes, the framework is called flexible, otherwise rigid. For a fixed graph, either all generic frameworks are rigid, or all generic ones are flexible. However, non-generic realizations might behave differently yielding for instance paradoxical motions. A few years ago, we have characterized the existence of a (non-generic) flexible realization in the plane for a given graph in terms of special edge colorings, called NAC-colorings. Here we summarize this surprising interplay between combinatorics and geometry and its various extensions shall be presented. We focus also on polyhedra with triangular faces, which can be considered as bar-joint frameworks in the 3-space. In particular, we mention a new result on the smallest flexible polyhedron without self-intersections.

Název v anglickém jazyce

Paradoxical flexibility: frameworks and polyhedra

Popis výsledku anglicky

One of the main questions of rigidity theory is whether a bar-joint framework, which is a graph with a realization of its vertices in the d-dimensional space, allows a continuous deformation preserving the distances between adjacent vertices. If yes, the framework is called flexible, otherwise rigid. For a fixed graph, either all generic frameworks are rigid, or all generic ones are flexible. However, non-generic realizations might behave differently yielding for instance paradoxical motions. A few years ago, we have characterized the existence of a (non-generic) flexible realization in the plane for a given graph in terms of special edge colorings, called NAC-colorings. Here we summarize this surprising interplay between combinatorics and geometry and its various extensions shall be presented. We focus also on polyhedra with triangular faces, which can be considered as bar-joint frameworks in the 3-space. In particular, we mention a new result on the smallest flexible polyhedron without self-intersections.

Druh

D - Stať ve sborníku

CEP obor

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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 statě ve sborníku

10th Czech-Slovak conference on geometry and graphics 2024

ISBN

978-80-8208-145-2

ISSN

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e-ISSN

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Počet stran výsledku

10

Strana od-do

29-38

Název nakladatele

Vydavateľstvo Slovak Chemistry Library

Místo vydání

Bratislava

Místo konání akce

Plzeň

Datum konání akce

9. 9. 2024

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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