2016 Lecture 7 : The Probabilistic Method
نویسنده
چکیده
We now move on to a very interesting and powerful technique in combinatorics, called the probabilistic method. There is an excellent (really excellent!) textbook written by Noga Alon and Joel Spencer [AS16]. In fact, most materials that we will cover are from [AS16]. The method works as follows. Our goal is to prove the existence of certain object or structure with desired properties. We start by define an appropriate probability space and then show that the desired properties hold with strictly positive probability. We will illustrate the method by a result due to Erdős which is regarded as the initiation of the probabilistic method.
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