Jarque i Ribera, XavierMartínez de Albéniz, F. JavierCamacho Martı́n, Laura2021-04-092021-04-092020-06https://hdl.handle.net/2445/176011Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Xavier Jarque i Ribera i F. Javier Martínez de Albéniz[en] In this project we study minimun cost spanning tree problems and how to associate them with a cooperative game of transferable utility. Some real economic situations such as the construction of an electricity network for the supply of energy to an entire village from a common power station can be modelled by these problems. This case was studied by Dutta and Kar (2004). On the one hand, we define two algorithms capable of obtaining a minimum cost spanning tree of a connected graph, namely Prim’s (1957) and Kruskal’s (1956). On the other hand, we explain a series of cost allocation rules, which are interpreted under the prism of cooperative games. A series of properties are detailed to see which of these properties determine them. We also study the irreducible form introduced by Bird (1976) associated with a minimum cost spanning tree problem. We see how to associate one to each problem and analyze the equivalence between rules in this irreducible form.55 p.application/pdfcatcc-by-nc-nd (c) Laura Camacho Martı́n, 2020http://creativecommons.org/licenses/by-nc-nd/3.0/es/Arbres (Teoria de grafs)Treballs de fi de grauJocs cooperatius (Matemàtica)Xarxes elèctriquesTrees (Graph theory)Bachelor's thesesCooperative games (Mathematics)Electric networksinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess