Abstract
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 Δ(G − v)·d(v)/2 by solving the 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.
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Chimani, M., Hliněný, P., Mutzel, P. (2009). Approximating the Crossing Number of Apex Graphs. In: Tollis, I.G., Patrignani, M. (eds) Graph Drawing. GD 2008. Lecture Notes in Computer Science, vol 5417. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00219-9_42
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DOI: https://doi.org/10.1007/978-3-642-00219-9_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00218-2
Online ISBN: 978-3-642-00219-9
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