--- res: bibo_abstract: - 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.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Radoslav foaf_name: Fulek, Radoslav foaf_surname: Fulek foaf_workInfoHomepage: http://www.librecat.org/personId=39F3FFE4-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0001-8485-1774 - foaf_Person: foaf_givenName: Jan foaf_name: Kynčl, Jan foaf_surname: Kynčl bibo_doi: 10.4230/LIPIcs.SoCG.2018.39 bibo_volume: 99 dct_date: 2018^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/978-3-95977-066-8 dct_language: eng dct_publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik@ dct_title: Hanani-Tutte for approximating maps of graphs@ ...