A project submitted in partial fulllment of the requirement
No Thumbnail Available
Date
2014-02-27
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Addis Ababa University
Abstract
Ramsey Theory is named after Frank Plumpton Ramsey a young man was
especially interested in logical and philosophy. Ramsey died at the age of 26
in 1930 the same year that his paper on a problem of formal logic was pub-
lished. His paper catalyzed the development of the mathematics _eld now
known as Ramsey Theory. Problem in Ramsey Theory typically ask a ques-
tion of the form: How many people are required at gathering so that there
must exist either three mutual acquaintances or three mutual strangers? We
can rephrase this question as a problem in Ramsey Theory: How many ver-
tices do you need in edge 2 colored complete graphs for it to be necessary
that there be either a red K3 (people who know each other) or a blue K3
(people who do not know each other)? While many results in the subjects are
published each year, there are many questions whose answer remains elusive.
Ramsey Theory has played an important role in a plethora of mathematics
development throughout the last century. Ramsey Theory is concerned with
the preservation of structure under partition it is the study of unavoidable
regularity in large structures. In this project, I explore some of the core ideas
underpinning Ramsey Theory and present a variety of problem to which it
can provide interesting and elegant solution. Also we have see, the Ramsey
number R(k; l) is the smallest natural number n such that in any red and
blue coloring of the edges of the complete graph on n vertices, we are guar-
anteed to _nd either a red Kk or a blue Kl. Furthermore, we have discussed
a multi-color example R(3; 3; 3) = 17, generalization of Ramsey Theorem
and in_nite Ramsey Theory. Some Known Ramsey Theorem for bound on
classical Ramsey numbers are included.
Description
Keywords
The undersigned hereby, certify that they have read and recommend