eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-06-08
27:1
27:14
10.4230/LIPIcs.SoCG.2018.27
article
Embedding Graphs into Two-Dimensional Simplicial Complexes
Verdière, Éric Colin de
Magnard, Thomas
Mohar, Bojan
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).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol099-socg2018/LIPIcs.SoCG.2018.27/LIPIcs.SoCG.2018.27.pdf
computational topology
embedding
simplicial complex
graph
surface