About: The Planar Slope Number of Planar Partial 3-Trees of Bounded Degree

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	It is known that every planar graph has a planar embedding where edges are represented by non-crossing straight-line segments. We study the planar slope number, i.e., the minimum number of distinct edge-slopes in such a drawing of a planar graph with maximum degree delta. We show that the planar slope number of every series-parallel graph of maximum degree three is three. We also show that the planar slope number of every planar partial 3-tree and also every plane partial 3-tree is at most 2^O(delta). In particular, we answer the question of Dujmović et al. [Computational Geometry 38 (3), pp. 194-212 (2007)] whether there is a function f such that plane maximal outerplanar graphs can be drawn using at most f(delta) slopes. It is known that every planar graph has a planar embedding where edges are represented by non-crossing straight-line segments. We study the planar slope number, i.e., the minimum number of distinct edge-slopes in such a drawing of a planar graph with maximum degree delta. We show that the planar slope number of every series-parallel graph of maximum degree three is three. We also show that the planar slope number of every planar partial 3-tree and also every plane partial 3-tree is at most 2^O(delta). In particular, we answer the question of Dujmović et al. [Computational Geometry 38 (3), pp. 194-212 (2007)] whether there is a function f such that plane maximal outerplanar graphs can be drawn using at most f(delta) slopes. (en)
Title	The Planar Slope Number of Planar Partial 3-Trees of Bounded Degree The Planar Slope Number of Planar Partial 3-Trees of Bounded Degree (en)
skos:prefLabel	The Planar Slope Number of Planar Partial 3-Trees of Bounded Degree The Planar Slope Number of Planar Partial 3-Trees of Bounded Degree (en)
skos:notation	RIV/00216208:11320/10:10051697!RIV11-MSM-11320___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(1M0545), Z(MSM0021620838)
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Jelínek, Vít Kratochvíl, Jan Jelínková, Eva Lidický, Bernard Tesař, Marek Vyskočil, Tomáš
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	279066
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/10:10051697
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	planar slope number; slopes; planar graphs; graph drawing (en)
http://linked.open.../riv/klicoveSlovo	slopes graph drawing planar graphs planar slope number
http://linked.open...ontrolniKodProRIV	[4D645296A5E6]
http://linked.open...v/mistoKonaniAkce	Chicago, USA
http://linked.open...i/riv/mistoVydani	Berlín, Německo
http://linked.open...i/riv/nazevZdroje	Graph Drawing
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	6 (xsd:int)
http://linked.open...cetTvurcuVysledku	6 (xsd:int)
http://linked.open...vavai/riv/projekt	Institute for Theoretical Computer Science
http://linked.open...UplatneniVysledku	2010
http://linked.open...iv/tvurceVysledku	Jelínek, Vít Jelínková, Eva Kratochvíl, Jan Lidický, Bernard Tesař, Marek Vyskočil, Tomáš
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open...ain/vavai/riv/wos	000279285200027
http://linked.open.../riv/zahajeniAkce	2009-09-22 (xsd:date)
http://linked.open...n/vavai/riv/zamer	Moderní metody, struktury a systémy informatiky
issn	0302-9743
number of pages	12 (xsd:int)
http://purl.org/ne...btex#hasPublisher	Springer-Verlag
https://schema.org/isbn	978-3-642-11804-3
http://localhost/t...ganizacniJednotka	11320

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