Quasirandom Graphs and the Pantograph Equation

Asaf Shapira; Mykhaylo Tyomkyn

doi:https://doi.org/10.1080/00029890.2021.1926187

Quasirandom Graphs and the Pantograph Equation

Asaf Shapira, Mykhaylo Tyomkyn

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	630-639
Number of pages	10
Journal	American Mathematical Monthly
Volume	128
Issue number	7
DOIs	https://doi.org/10.1080/00029890.2021.1926187
State	Published - 2021

Keywords

30D20
MSC: Primary 05C35
Secondary 05C80

All Science Journal Classification (ASJC) codes

General Mathematics

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https://doi.org/10.1080/00029890.2021.1926187

Cite this

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AB - 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.

KW - 30D20

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KW - Secondary 05C80

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EP - 639

JO - American Mathematical Monthly

JF - American Mathematical Monthly

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ER -

Quasirandom Graphs and the Pantograph Equation

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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