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dc.contributor.authorBose, Prosenjit
dc.contributor.authorDujmovic, Vida
dc.contributor.authorHurtado Díaz, Fernando Alfredo
dc.contributor.authorLangerman, Stefan
dc.contributor.authorMorin, Pat
dc.contributor.authorWood, David
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II
dc.date.accessioned2010-10-08T11:52:25Z
dc.date.available2010-10-08T11:52:25Z
dc.date.created2009-12
dc.date.issued2009-12
dc.identifier.citationBose, P. [et al.]. A polynomial bound for untangling geometric planar graphs. "Discrete and computational geometry", Desembre 2009, vol. 42, núm. 4, p. 570-585.
dc.identifier.issn0179-5376
dc.identifier.urihttp://hdl.handle.net/2117/9583
dc.description.abstractTo untangle a geometric graph means to move some of the vertices so that the resulting geometric graph has no crossings. Pach and Tardos (Discrete Comput. Geom. 28(4): 585–592, 2002) asked if every n-vertex geometric planar graph can be untangled while keeping at least $n^\in{}$ vertices fixed. We answer this question in the affirmative with ∊ = 1/4. The previous best known bound was Ω$(\sqrt{log\,n/log\,log\,n})$. We also consider untangling geometric trees. It is known that every n-vertex geometric tree can be untangled while keeping at least $(\sqrt{n/3})$ vertices fixed, while the best upper bound was O$((n\,log\,n)^{2/3})$. We answer a question of Spillner and Wolff (http://arxiv.org/abs/0709.0170) by closing this gap for untangling trees. In particular, we show that for infinitely many values of n, there is an n-vertex geometric tree that cannot be untangled while keeping more than $3(\sqrt{n}-1)$ vertices fixed.
dc.format.extent16 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria convexa i discreta
dc.subject.lcshCrossings
dc.subject.lcshDiscrete geometry
dc.subject.lcshGraph theory
dc.subject.lcshPolynomials
dc.titleA polynomial bound for untangling geometric planar graphs
dc.typeArticle
dc.subject.lemacGrafs, Teoria de
dc.subject.lemacGeometria discreta
dc.subject.lemacPolinomis
dc.contributor.groupUniversitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
dc.identifier.doi10.1007/s00454-008-9125-3
dc.relation.publisherversionhttp://arxiv.org/PS_cache/arxiv/pdf/0710/0710.1641v2.pdf
dc.rights.accessOpen Access
drac.iddocument3257231
dc.description.versionPostprint (published version)
upcommons.citation.authorBose, P.; Dujmovic, V.; Hurtado, F.; Langerman, S.; Morín, P.; Wood, D.
upcommons.citation.publishedtrue
upcommons.citation.publicationNameDiscrete and computational geometry
upcommons.citation.volume42
upcommons.citation.number4
upcommons.citation.startingPage570
upcommons.citation.endingPage585


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