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Threshold phenomena in random graphs Redón Orriols, Nil Universitat Politècnica de Catalunya. Departament de Matemàtiques Rué Perna, Juan José Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs Graph theory Random graphs Threshold phenomena Giant component. Grafs, Teoria de Classificació AMS::05 Combinatorics::05C Graph theory In the 1950s, random graphs appeared for the first time in a result of the prolific hungarian mathematician Pál Erd\H{o}s. Since then, interest in random graph theory has only grown up until now. In its first stages, the basis of its theory were set, while they were mainly used in probability and combinatorics theory. However, with the new century and the boom of technologies like the World Wide Web, random graphs are even more important since they are extremely useful to handle problems in fields like network and communication theory. Because of this fact, nowadays random graphs are widely studied by the mathematical community around the world and new promising results have been recently achieved, showing an exciting future for this field. In this bachelor thesis, we focus our study on the threshold phenomena for graph properties within random graphs. 2019-07 Bachelor thesis https://hdl.handle.net/2117/166431 FME-1781 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Open Access application/pdf Universitat Politècnica de Catalunya