Quasirandom Graphs and the Pantograph Equation
Combinatorics
2021-05-26 v2
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.
Keywords
Cite
@article{arxiv.2101.08173,
title = {Quasirandom Graphs and the Pantograph Equation},
author = {Asaf Shapira and Mykhaylo Tyomkyn},
journal= {arXiv preprint arXiv:2101.08173},
year = {2021}
}
Comments
To appear in Amer. Math. Monthly