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dc.contributorSerra Albó, Oriol
dc.contributorVena Cros, Lluís
dc.contributor.authorLamaison Vidarte, Ander
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.date.accessioned2015-07-31T12:35:00Z
dc.date.available2015-07-31T12:35:00Z
dc.date.issued2015-07
dc.identifier.urihttp://hdl.handle.net/2117/76479
dc.description.abstractIn 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.isoeng
dc.publisherUniversitat Politècnica de Catalunya
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
dc.subject.lcshGraph theory
dc.subject.otherPseudorandom
dc.subject.otherRegularity lemma
dc.subject.otherRemoval lemma
dc.subject.otherSparse graphs
dc.titleRemoval lemmas in sparse graphs
dc.typeBachelor thesis
dc.subject.lemacGrafs, Teoria de
dc.subject.amsClassificació AMS::05 Combinatorics::05C Graph theory
dc.identifier.slugFME-1191
dc.rights.accessOpen Access
dc.date.updated2015-07-21T11:00:43Z
dc.audience.educationlevelGrau
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
dc.audience.degreeGRAU EN MATEMÀTIQUES (Pla 2009)


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