TY - JOUR
T1 - Quasirandom Graphs and the Pantograph Equation
AU - Shapira, Asaf
AU - Tyomkyn, Mykhaylo
N1 - Publisher Copyright:
© 2021 The Author(s). Published with license by Taylor & Francis Group, LLC.
PY - 2021
Y1 - 2021
N2 - 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.
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
KW - MSC: Primary 05C35
KW - Secondary 05C80
UR - http://www.scopus.com/inward/record.url?scp=85113821759&partnerID=8YFLogxK
U2 - 10.1080/00029890.2021.1926187
DO - 10.1080/00029890.2021.1926187
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C2 - 34456338
AN - SCOPUS:85113821759
SN - 0002-9890
VL - 128
SP - 630
EP - 639
JO - American Mathematical Monthly
JF - American Mathematical Monthly
IS - 7
ER -