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Removal lemmas in sparse graphs
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) |