Susan Fettes

Abstract

The classical Ramsey Number R(3, 3, 3, 3), which is the smallest positive integer n such that any edge coloring with four colors of the complete graph on n vertices must contain at least one monochromatic triangle, is discussed. Basic facts and graph theoretic definitions are given. Papers concerning triangle-free colorings are presented in a historical overview. Mathematical theory underlying the main result of the thesis, which is Richard Kramers unpublished result, i?(3,3,3,3) < 62, is given. The algorithms for the com putational verification of this result are presented along with a discussion of the software tools that were utilized to obtain it.

Library of Congress Subject Headings

Ramsey numbers; Ramsey theory; Graph theory

Publication Date

2001

Document Type

Thesis

Department, Program, or Center

Computer Science (GCCIS)

Advisor

Radziszowski, Stanislaw

Advisor/Committee Member

Hemaspaandra, Edith

Advisor/Committee Member

Vallino, James

Comments

Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works. Physical copy available through RIT's The Wallace Library at: QA166 .F488 2001

Campus

RIT – Main Campus

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