Abstract

Establishing the values of Ramsey numbers is, in general, a difficult task from the computational point of view. Over the years, researchers have developed methods to tackle this problem exhaustively in ways that require intensive computations. These methods are often backed by theoretical results that allow us to cut the search space down to a size that is within the limits of current computing capacity.

This thesis focuses on developing algorithms and applying them to generate Ramsey colorings avoiding cycles. It adds to a recent trend of interest in this particular area of finite Ramsey theory. Our main contributions are the enumeration of all (C_5,C_5,C_5;n) Ramsey colorings and the study of the Ramsey numbers R(C_4,C_4,K_4) and R4(C_5).

Library of Congress Subject Headings

Ramsey numbers; Graph coloring; Paths and cycles (Graph theory)

Publication Date

5-2015

Document Type

Thesis

Student Type

Graduate

Degree Name

Computer Science (MS)

Department, Program, or Center

Computer Science (GCCIS)

Advisor

Stanislaw P. Radziszowski

Advisor/Committee Member

Edith Hemaspaandra

Advisor/Committee Member

Ivona Bezakova

Comments

Physical copy available from RIT's Wallace Library at QA166 .N378 2015

Campus

RIT – Main Campus

Plan Codes

COMPSCI-MS

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