The Probabilistic Method and Random Graphs
The probabilistic method in combinatorics is a nonconstructive tool popularized through the work of Paul Erd˝os. Many difficult problems can be solved through a relatively simple application of probability theory that can lead to solutions which are better than known constructive methods. This t...
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2012
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| Online Access: | http://hdl.handle.net/1993/9228 |
| Summary: | The probabilistic method in combinatorics is a nonconstructive tool popularized
through the work of Paul Erd˝os. Many difficult problems can be solved
through a relatively simple application of probability theory that can lead to
solutions which are better than known constructive methods.
This thesis presents some of the basic tools used throughout the probabilistic
method along with some of the applications of the probabilistic method
throughout the fields of Ramsey theory, graph theory and other areas of combinatorial
analysis.
Then the topic of random graphs is covered. The theory of random graphs
was founded during the late fifties and early sixties to study questions involving
the effect of probability distributions upon graphical properties. This thesis
presents some of the basic results involving graph models and graph properties. |
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