• Media type: Text; Electronic Conference Proceeding; E-Article
  • Title: Embedding Graphs into Embedded Graphs
  • Contributor: Fulek, Radoslav [Author]
  • imprint: Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2017
  • Language: English
  • DOI: https://doi.org/10.4230/LIPIcs.ISAAC.2017.34
  • Keywords: Weakly simple polygons ; C-planarity ; Graph embedding
  • Origination:
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  • Description: A (possibly degenerate) drawing of a graph G in the plane is approximable by an embedding if it can be turned into an embedding by an arbitrarily small perturbation. We show that testing, whether a drawing of a planar graph G in the plane is approximable by an embedding, can be carried out in polynomial time, if a desired embedding of G belongs to a fixed isotopy class, i.e., the rotation system (or equivalently the faces) of the embedding of G and the choice of outer face are fixed. In other words, we show that c-planarity with embedded pipes is tractable for graphs with fixed embeddings. To the best of our knowledge an analogous result was previously known essentially only when G is a cycle.
  • Access State: Open Access