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Embedding Graphs into Embedded Graphs

Author Radoslav Fulek

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  • Graph embedding
  • C-planarity
  • Weakly simple polygons

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Abstract

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.

Cite As Get BibTex

Radoslav Fulek. Embedding Graphs into Embedded Graphs. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 34:1-34:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.ISAAC.2017.34

Author Details

Radoslav Fulek

References

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