Graph Theory
The Graph Theory course covers different aspects of graphs, as well as some of their more important applications. The course is split into four parts. In the first part, we give a short introduction to Graph Theory, presenting classical results such as the theorems of Hall, Menger and Dirac. In the last three parts, we approach the notion of graph from different perspectives: the probabilistic one (random graphs, probabilistic methods and models for complex networks), the spectral one (graph spectrum, isoperimetry, random walks and clustering) and the extremal one (Turán-type problems, Szemerédi regularity lemma and removal lemma). No previous knowledge on the subject is required.
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