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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
  • Vertex insertion approximates the crossing number of apex graphs
  • Vertex insertion approximates the crossing number of apex graphs (en)
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  • Vertex insertion approximates the crossing number of apex graphs
  • Vertex insertion approximates the crossing number of apex graphs (en)
skos:notation
  • RIV/00216224:14330/12:00057323!RIV13-GA0-14330___
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  • 3
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  • 177342
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  • RIV/00216224:14330/12:00057323
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  • crossing number; crossing minimization; apex graph (en)
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  • NL - Nizozemsko
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  • [188EE25AD8B3]
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  • European Journal of Combinatorics
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  • 33
http://linked.open...iv/tvurceVysledku
  • Chimani, Markus
  • Hliněný, Petr
  • Mutzel, Petra
http://linked.open...ain/vavai/riv/wos
  • 000299858000005
issn
  • 0195-6698
number of pages
http://bibframe.org/vocab/doi
  • 10.1016/j.ejc.2011.09.009
http://localhost/t...ganizacniJednotka
  • 14330
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