License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2018.27
URN: urn:nbn:de:0030-drops-87401
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Verdière, Éric Colin de ; Magnard, Thomas ; Mohar, Bojan

Embedding Graphs into Two-Dimensional Simplicial Complexes

LIPIcs-SoCG-2018-27.pdf (0.5 MB)


We consider the problem of deciding whether an input graph G admits a topological embedding into a two-dimensional simplicial complex C. This problem includes, among others, the embeddability problem of a graph on a surface and the topological crossing number of a graph, but is more general.
The problem is NP-complete when C is part of the input, and we give a polynomial-time algorithm if the complex C is fixed.
Our strategy is to reduce the problem to an embedding extension problem on a surface, which has the following form: Given a subgraph H' of a graph G', and an embedding of H' on a surface S, can that embedding be extended to an embedding of G' on S? Such problems can be solved, in turn, using a key component in Mohar's algorithm to decide the embeddability of a graph on a fixed surface (STOC 1996, SIAM J. Discr. Math. 1999).

BibTeX - Entry

  author =	{{\'E}ric Colin de Verdi{\`e}re and Thomas Magnard and Bojan Mohar},
  title =	{{Embedding Graphs into Two-Dimensional Simplicial Complexes}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{27:1--27:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-87401},
  doi =		{10.4230/LIPIcs.SoCG.2018.27},
  annote =	{Keywords: computational topology, embedding, simplicial complex, graph, surface}

Keywords: computational topology, embedding, simplicial complex, graph, surface
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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