{"quality_controlled":"1","day":"01","abstract":[{"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 &quot;pipes&quot; 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.","lang":"eng"}],"status":"public","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"date_updated":"2021-01-12T06:53:36Z","intvolume":"        99","volume":99,"project":[{"grant_number":"M02281","call_identifier":"FWF","name":"Eliminating intersections in drawings of graphs","_id":"261FA626-B435-11E9-9278-68D0E5697425"}],"has_accepted_license":"1","date_published":"2018-01-01T00:00:00Z","ddc":["510"],"file":[{"checksum":"f1b94f1a75b37c414a1f61d59fb2cd4c","creator":"dernst","file_id":"5701","access_level":"open_access","relation":"main_file","date_updated":"2020-07-14T12:45:19Z","content_type":"application/pdf","file_size":718857,"file_name":"2018_LIPIcs_Fulek.pdf","date_created":"2018-12-17T12:33:52Z"}],"year":"2018","date_created":"2018-12-11T11:45:04Z","article_number":"39","alternative_title":["Leibniz International Proceedings in Information, LIPIcs"],"department":[{"_id":"UlWa"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publist_id":"7735","author":[{"first_name":"Radoslav","orcid":"0000-0001-8485-1774","full_name":"Fulek, Radoslav","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","last_name":"Fulek"},{"full_name":"Kynčl, Jan","first_name":"Jan","last_name":"Kynčl"}],"language":[{"iso":"eng"}],"file_date_updated":"2020-07-14T12:45:19Z","publication_status":"published","conference":{"start_date":"2018-06-11","location":"Budapest, Hungary","end_date":"2018-06-14","name":"SoCG: Symposium on Computational Geometry"},"oa":1,"scopus_import":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","citation":{"apa":"Fulek, R., &#38; 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. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.39\">https://doi.org/10.4230/LIPIcs.SoCG.2018.39</a>","short":"R. Fulek, J. Kynčl, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018.","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.","mla":"Fulek, Radoslav, and Jan Kynčl. <i>Hanani-Tutte for Approximating Maps of Graphs</i>. Vol. 99, 39, 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>.","chicago":"Fulek, Radoslav, and Jan Kynčl. “Hanani-Tutte for Approximating Maps of Graphs,” Vol. 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.39\">https://doi.org/10.4230/LIPIcs.SoCG.2018.39</a>.","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.","ama":"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>"},"type":"conference","oa_version":"Published Version","title":"Hanani-Tutte for approximating maps of graphs","month":"01","publication_identifier":{"isbn":["978-3-95977-066-8"]},"doi":"10.4230/LIPIcs.SoCG.2018.39","_id":"185"}