Knauer, KoljaMoles Gené, Oriol2022-07-142022-07-142022-01-24https://hdl.handle.net/2445/187688Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Kolja Knauer[en] This project is about directed cuts, directed joins and their packings. We study the open problem of Woodall’s Conjecture, a problem studied by many authors to such an extent that it even has a $5000 dollars prize for his demonstration set by G. Cornuéjols. We will also cover the Lucchesi-Younger Theorem proof which can be seen as a dual result of the conjecture and the counterexample for the Edmonds-Giles Conjecture, the weighted version of Woodall’s Conjecture. Besides studying the theory we have set ourselves the goal of proposing a program that given a graph, checks if all of its orientations validate the Woodall’s Conjecture. This program should be able to prove the conjecture, up to a certain number of vertices, by testing all the different combinations.43 p.application/pdfengcc-by-nc-nd (c) Oriol Moles Gené, 2022http://creativecommons.org/licenses/by-nc-nd/3.0/es/Teoria de grafsTreballs de fi de grauAnàlisi combinatòriaGraph theoryBachelor's thesesCombinatorial analysisinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess