--- _id: '185' abstract: - lang: eng text: 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. alternative_title: - Leibniz International Proceedings in Information, LIPIcs article_number: '39' author: - first_name: Radoslav full_name: Fulek, Radoslav id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87 last_name: Fulek orcid: 0000-0001-8485-1774 - first_name: Jan full_name: Kynčl, Jan last_name: Kynčl citation: ama: 'Fulek R, Kynčl J. Hanani-Tutte for approximating maps of graphs. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:10.4230/LIPIcs.SoCG.2018.39' apa: 'Fulek, R., & Kynčl, J. (2018). Hanani-Tutte for approximating maps of graphs (Vol. 99). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.39' chicago: Fulek, Radoslav, and Jan Kynčl. “Hanani-Tutte for Approximating Maps of Graphs,” Vol. 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.39. ieee: 'R. Fulek and J. Kynčl, “Hanani-Tutte for approximating maps of graphs,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99.' ista: 'Fulek R, Kynčl J. 2018. Hanani-Tutte for approximating maps of graphs. SoCG: Symposium on Computational Geometry, Leibniz International Proceedings in Information, LIPIcs, vol. 99, 39.' mla: Fulek, Radoslav, and Jan Kynčl. Hanani-Tutte for Approximating Maps of Graphs. Vol. 99, 39, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, doi:10.4230/LIPIcs.SoCG.2018.39. short: R. Fulek, J. Kynčl, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. conference: end_date: 2018-06-14 location: Budapest, Hungary name: 'SoCG: Symposium on Computational Geometry' start_date: 2018-06-11 date_created: 2018-12-11T11:45:04Z date_published: 2018-01-01T00:00:00Z date_updated: 2021-01-12T06:53:36Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2018.39 file: - access_level: open_access checksum: f1b94f1a75b37c414a1f61d59fb2cd4c content_type: application/pdf creator: dernst date_created: 2018-12-17T12:33:52Z date_updated: 2020-07-14T12:45:19Z file_id: '5701' file_name: 2018_LIPIcs_Fulek.pdf file_size: 718857 relation: main_file file_date_updated: 2020-07-14T12:45:19Z has_accepted_license: '1' intvolume: ' 99' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '01' oa: 1 oa_version: Published Version project: - _id: 261FA626-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02281 name: Eliminating intersections in drawings of graphs publication_identifier: isbn: - 978-3-95977-066-8 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik publist_id: '7735' quality_controlled: '1' scopus_import: 1 status: public title: Hanani-Tutte for approximating maps of graphs tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 99 year: '2018' ...