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 Mathematical theory underlying the main result of the thesis, which is Richard Kramers unpublished result, i?(3,3,3,3) 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
Department, Program, or Center
Computer Science (GCCIS)
Fettes, Susan, "On the classical Ramsey Number R(3,3,3,3)" (2001). Thesis. Rochester Institute of Technology. Accessed from
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