On the classical Ramsey Number R(3,3,3,3)

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Title: On the classical Ramsey Number R(3,3,3,3)
Author: Fettes, Susan
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 Mathematical theory underlying the main result of the thesis, which is Richard Kramers unpublished result, i?(3,3,3,3) 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.
Record URI: http://hdl.handle.net/1850/14341
Date: 2001

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