Three-Color Rado Numbers for an Inequality

Author

Brenda Johnson, South Dakota State University

Document Type

Thesis - University Access Only

Award Date

2004

Degree Name

Master of Science (MS)

Department / School

Mathematics and Statistics

First Advisor

Daniel Schaal

Abstract

Given a system of linear equations or inequalities, the least integer n, provided that it exists, such that for every t-coloring of the set { 1, 2, ... , n} there exists a monochromatic solution to the system is called the t-color Rado number for the system. If there does not exist a least integer n, then we say that the t-color Rado number for the system is infinite. The two-color Rado number of the inequality x₁ + x₂ + · · · + X_m-1 < x_m, where x_i ≠ x_j when i ≠ j, has already been determined and published. In addition, the structure of the longest two-coloring that avoids a monochromatic solution to the inequality was determined. In this paper, we will present the three-color Rado number of the same inequality and also the structure of the longest three-coloring that avoids a monochromatic solution to the inequality.

Library of Congress Subject Headings

Inequalities (Mathematics)
Ramsey theory.
Combinatorial analysis.

Publisher

South Dakota State University

Recommended Citation

Johnson, Brenda, "Three-Color Rado Numbers for an Inequality" (2004). Electronic Theses and Dissertations. 1098.
https://openprairie.sdstate.edu/etd2/1098