dc.contributor Serra Albó, Oriol dc.contributor Vena Cros, Lluís dc.contributor.author Lamaison Vidarte, Ander dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV dc.date.accessioned 2015-07-31T12:35:00Z dc.date.available 2015-07-31T12:35:00Z dc.date.issued 2015-07 dc.identifier.uri http://hdl.handle.net/2117/76479 dc.description.abstract In this work we explain and prove the graph removal lemma, both in its dense and sparse cases, and show how these can be applied to finite groups to obtain arithmetic removal lemmas. We show how the concept of regularity plays a crucial role in the proof of the removal lemma. We explain the motivation behind the sparse case, and the importance of pseudorandom graphs in sparse versions of the removal lemma. Finally, we show how the removal lemma, both in its graph and arithmetic versions, can be used to prove Roth's theorem, that is, the existence of 3-term arithmetic progressions in any dense subset of the natural numbers. dc.language.iso eng dc.publisher Universitat Politècnica de Catalunya dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs dc.subject.lcsh Graph theory dc.subject.other Pseudorandom dc.subject.other Regularity lemma dc.subject.other Removal lemma dc.subject.other Sparse graphs dc.title Removal lemmas in sparse graphs dc.type Bachelor thesis dc.subject.lemac Grafs, Teoria de dc.subject.ams Classificació AMS::05 Combinatorics::05C Graph theory dc.identifier.slug FME-1191 dc.rights.access Open Access dc.date.updated 2015-07-21T11:00:43Z dc.audience.educationlevel Grau dc.audience.mediator Universitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística dc.audience.degree GRAU EN MATEMÀTIQUES (Pla 2009)
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