Català   Castellano   English
 Empreu aquest identificador per citar o enllaçar aquest ítem: http://hdl.handle.net/2117/9583

Arxiu Descripció MidaFormat
 Citació: Bose, P. [et al.]. A polynomial bound for untangling geometric planar graphs. "Discrete and computational geometry", Desembre 2009, vol. 42, núm. 4, p. 570-585. Títol: A polynomial bound for untangling geometric planar graphs Autor: Bose, Prosenjit; Dujmovic, Vida; Hurtado Díaz, Fernando Alfredo ; Langerman, Stefan; Morin, Pat; Wood, David Data: des-2009 Tipus de document: Article Resum: To 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. ISSN: 0179-5376 URI: http://hdl.handle.net/2117/9583 DOI: 10.1007/s00454-008-9125-3 Versió de l'editor: http://arxiv.org/PS_cache/arxiv/pdf/0710/0710.1641v2.pdf Apareix a les col·leccions: DCCG - Grup de recerca en geometria computacional, combinatoria i discreta. Articles de revistaDepartaments de Matemàtica Aplicada. Articles de revistaAltres. Enviament des de DRAC Comparteix: