Quasirandom Graphs and the Pantograph Equation

Asaf Shapira, Mykhaylo Tyomkyn

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)630-639
Number of pages10
JournalAmerican Mathematical Monthly
Issue number7
StatePublished - 2021


FundersFunder number
NSF-BSF20196, DYNASNET 810115
Horizon 2020 Framework Programme633509, 823748, 810115
European Research Council863438
Israel Science Foundation1028/16


    • 30D20
    • MSC: Primary 05C35
    • Secondary 05C80


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