Quasirandom Graphs and the Pantograph Equation

The pantograph differential equation and its solution, the deformed exponential function, are remarkable objects that appear in areas as diverse as combinatorics, number theory, statistical mechanics, and electrical engineering. In this article, we describe a new surprising application of these obje...

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Detalles Bibliográficos
Autores principales: Shapira, Asaf, Tyomkyn, Mykhaylo
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Taylor & Francis 2021
Materias:
Original Articles
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8388949/
https://www.ncbi.nlm.nih.gov/pubmed/34456338
http://dx.doi.org/10.1080/00029890.2021.1926187
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author Shapira, Asaf
Tyomkyn, Mykhaylo
author_facet Shapira, Asaf
Tyomkyn, Mykhaylo
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description The pantograph differential equation and its solution, the deformed exponential function, are remarkable objects that appear in areas as diverse as combinatorics, number theory, statistical mechanics, and electrical engineering. In this article, we describe a new surprising application of these objects in graph theory, by showing that the set of all cliques is not forcing for quasirandomness. This provides a natural example of an infinite family of graphs, which is not forcing, and answers a natural question posed by P. Horn.
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spelling pubmed-83889492021-08-27 Quasirandom Graphs and the Pantograph Equation Shapira, Asaf Tyomkyn, Mykhaylo Am Math Mon Original Articles The pantograph differential equation and its solution, the deformed exponential function, are remarkable objects that appear in areas as diverse as combinatorics, number theory, statistical mechanics, and electrical engineering. In this article, we describe a new surprising application of these objects in graph theory, by showing that the set of all cliques is not forcing for quasirandomness. This provides a natural example of an infinite family of graphs, which is not forcing, and answers a natural question posed by P. Horn. Taylor & Francis 2021-08-06 /pmc/articles/PMC8388949/ /pubmed/34456338 http://dx.doi.org/10.1080/00029890.2021.1926187 Text en © 2021 The Author(s). Published with license by Taylor & Francis Group, LLC. https://creativecommons.org/licenses/by-nc-nd/4.0/This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0 (https://creativecommons.org/licenses/by-nc-nd/4.0/) ), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.
spellingShingle Original Articles
Shapira, Asaf
Tyomkyn, Mykhaylo
Quasirandom Graphs and the Pantograph Equation
title Quasirandom Graphs and the Pantograph Equation
title_full Quasirandom Graphs and the Pantograph Equation
title_fullStr Quasirandom Graphs and the Pantograph Equation
title_full_unstemmed Quasirandom Graphs and the Pantograph Equation
title_short Quasirandom Graphs and the Pantograph Equation
title_sort quasirandom graphs and the pantograph equation
topic Original Articles
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8388949/
https://www.ncbi.nlm.nih.gov/pubmed/34456338
http://dx.doi.org/10.1080/00029890.2021.1926187
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