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Formulas for two-color Rado numbers have been established for many families of linear equations. However, there are no explicit formulas for two-color Rado numbers for any nonlinear equations. In this paper, we will establish formulas for the two-color Rado numbers for three families of equations: x + y ^sup n^ = z, x + y ^sup 2^ + c = z, and x + y ^sup 2^ = az , where c and a are positive integers.[PUBLICATION ABSTRACT]

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Key topics
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Ramsey theory;
Ramsey;
Natural number;
Convergence;
Nonlinear system
Subject
Graphs;
Nonlinear equations
Identifier / keyword
Ramsey theory; Ramsey; Natural number; Convergence; Nonlinear system
Title
An Excursion into Nonlinear Ramsey Theory
Author
Doss, Adam; Saracino, Dan; Vestal, Donald L
Publication title
Graphs and Combinatorics; Tokyo
Volume
29
Issue
3
Pages
407-415
Publication year
2013
Publication date
May 2013
Publisher
Springer Nature B.V.
Place of publication
Tokyo
Country of publication
Netherlands
Publication subject
Mathematics, Mathematics--Computer Applications
ISSN
09110119
e-ISSN
14355914
Source type
Scholarly Journal
Language of publication
English
Document type
Feature
Document feature
References
DOI
https://doi.org/10.1007/s00373-012-1140-8
ProQuest document ID
1357222271
Document URL
https://www.proquest.com/scholarly-journals/excursion-into-nonlinear-ramsey-theory/docview/1357222271/se-2?accountid=208611
Copyright
Springer Japan 2013
Last updated
2023-11-24
Database
ProQuest One Academic