Hanani-Tutte for approximating maps of graphs
Leibniz International Proceedings in Information, LIPIcs
Fulek, Radoslav
Kynčl, Jan
ddc:510
We resolve in the affirmative conjectures of A. Skopenkov and Repovš (1998), and M. Skopenkov (2003) generalizing the classical Hanani-Tutte theorem to the setting of approximating maps of graphs on 2-dimensional surfaces by embeddings. Our proof of this result is constructive and almost immediately implies an efficient algorithm for testing whether a given piecewise linear map of a graph in a surface is approximable by an embedding. More precisely, an instance of this problem consists of (i) a graph G whose vertices are partitioned into clusters and whose inter-cluster edges are partitioned into bundles, and (ii) a region R of a 2-dimensional compact surface M given as the union of a set of pairwise disjoint discs corresponding to the clusters and a set of pairwise disjoint "pipes" corresponding to the bundles, connecting certain pairs of these discs. We are to decide whether G can be embedded inside M so that the vertices in every cluster are drawn in the corresponding disc, the edges in every bundle pass only through its corresponding pipe, and every edge crosses the boundary of each disc at most once.
Schloss Dagstuhl - Leibniz-Zentrum für Informatik
2018
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http://purl.org/coar/resource_type/c_5794
https://research-explorer.ista.ac.at/record/185
https://research-explorer.ista.ac.at/download/185/5701
Fulek R, Kynčl J. Hanani-Tutte for approximating maps of graphs. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2018.39">10.4230/LIPIcs.SoCG.2018.39</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.4230/LIPIcs.SoCG.2018.39
info:eu-repo/semantics/altIdentifier/isbn/978-3-95977-066-8
info:eu-repo/grantAgreement/FWF//M02281
info:eu-repo/semantics/openAccess