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  • We show that the crossing number of an apex graph, i.e.\ a graph $G$ from which only one vertex $v$ has to be removed to make it planar, can be approximated up to a factor of $\Delta(G-v)\cdot d(v)/2$ by solving the \emph{vertex inserting} problem, i.e.\ inserting a vertex plus incident edges into an optimally chosen planar embedding of a planar graph. Due to a recently developed polynomial algorithm for the latter problem, this establishes the first polynomial fixed-constant approximation algorithm for the crossing number problem of apex graphs with bounded degree.
  • We show that the crossing number of an apex graph, i.e.\ a graph $G$ from which only one vertex $v$ has to be removed to make it planar, can be approximated up to a factor of $\Delta(G-v)\cdot d(v)/2$ by solving the \emph{vertex inserting} problem, i.e.\ inserting a vertex plus incident edges into an optimally chosen planar embedding of a planar graph. Due to a recently developed polynomial algorithm for the latter problem, this establishes the first polynomial fixed-constant approximation algorithm for the crossing number problem of apex graphs with bounded degree. (en)
Title
  • Approximating the Crossing Number of Apex Graphs (poster)
  • Approximating the Crossing Number of Apex Graphs (poster) (en)
skos:prefLabel
  • Approximating the Crossing Number of Apex Graphs (poster)
  • Approximating the Crossing Number of Apex Graphs (poster) (en)
skos:notation
  • RIV/00216224:14330/09:00029117!RIV11-GA0-14330___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(1M0545), P(GA201/08/0308), S, Z(MSM0021622419)
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 303920
http://linked.open...ai/riv/idVysledku
  • RIV/00216224:14330/09:00029117
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • crossing number; crossing minimization; apex graph (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [A976AB59598C]
http://linked.open...v/mistoKonaniAkce
  • Heraklion, Greece
http://linked.open...i/riv/mistoVydani
  • Berlin
http://linked.open...i/riv/nazevZdroje
  • Symposium Graph Drawing 2008, Lecture Notes in Computer Science
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...iv/tvurceVysledku
  • Chimani, Markus
  • Hliněný, Petr
  • Mutzel, Petra
http://linked.open...vavai/riv/typAkce
http://linked.open...ain/vavai/riv/wos
  • 000264579700041
http://linked.open.../riv/zahajeniAkce
http://linked.open...n/vavai/riv/zamer
issn
  • 0302-9743
number of pages
http://purl.org/ne...btex#hasPublisher
  • Springer-Verlag
https://schema.org/isbn
  • 978-3-642-00218-2
http://localhost/t...ganizacniJednotka
  • 14330
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