{"citation":{"ieee":"R. Fulek, B. Gärtner, A. Kupavskii, P. Valtr, and U. Wagner, “The crossing Tverberg theorem,” in <i>35th International Symposium on Computational Geometry</i>, Portland, OR, United States, 2019, vol. 129, p. 38:1-38:13.","mla":"Fulek, Radoslav, et al. “The Crossing Tverberg Theorem.” <i>35th International Symposium on Computational Geometry</i>, vol. 129, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 38:1-38:13, doi:<a href=\"https://doi.org/10.4230/LIPICS.SOCG.2019.38\">10.4230/LIPICS.SOCG.2019.38</a>.","ista":"Fulek R, Gärtner B, Kupavskii A, Valtr P, Wagner U. 2019. The crossing Tverberg theorem. 35th International Symposium on Computational Geometry. SoCG 2019: Symposium on Computational Geometry, LIPIcs, vol. 129, 38:1-38:13.","ama":"Fulek R, Gärtner B, Kupavskii A, Valtr P, Wagner U. The crossing Tverberg theorem. In: <i>35th International Symposium on Computational Geometry</i>. Vol 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:38:1-38:13. doi:<a href=\"https://doi.org/10.4230/LIPICS.SOCG.2019.38\">10.4230/LIPICS.SOCG.2019.38</a>","apa":"Fulek, R., Gärtner, B., Kupavskii, A., Valtr, P., &#38; Wagner, U. (2019). The crossing Tverberg theorem. In <i>35th International Symposium on Computational Geometry</i> (Vol. 129, p. 38:1-38:13). Portland, OR, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPICS.SOCG.2019.38\">https://doi.org/10.4230/LIPICS.SOCG.2019.38</a>","short":"R. Fulek, B. Gärtner, A. Kupavskii, P. Valtr, U. Wagner, in:, 35th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 38:1-38:13.","chicago":"Fulek, Radoslav, Bernd Gärtner, Andrey Kupavskii, Pavel Valtr, and Uli Wagner. “The Crossing Tverberg Theorem.” In <i>35th International Symposium on Computational Geometry</i>, 129:38:1-38:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. <a href=\"https://doi.org/10.4230/LIPICS.SOCG.2019.38\">https://doi.org/10.4230/LIPICS.SOCG.2019.38</a>."},"page":"38:1-38:13","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"project":[{"_id":"261FA626-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Eliminating intersections in drawings of graphs","grant_number":"M02281"}],"publication":"35th International Symposium on Computational Geometry","alternative_title":["LIPIcs"],"scopus_import":1,"volume":129,"has_accepted_license":"1","type":"conference","department":[{"_id":"UlWa"}],"ddc":["000","510"],"status":"public","_id":"6647","file_date_updated":"2020-07-14T12:47:35Z","author":[{"orcid":"0000-0001-8485-1774","last_name":"Fulek","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","first_name":"Radoslav","full_name":"Fulek, Radoslav"},{"first_name":"Bernd","full_name":"Gärtner, Bernd","last_name":"Gärtner"},{"full_name":"Kupavskii, Andrey","first_name":"Andrey","last_name":"Kupavskii"},{"full_name":"Valtr, Pavel","first_name":"Pavel","last_name":"Valtr"},{"full_name":"Wagner, Uli","first_name":"Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","orcid":"0000-0002-1494-0568"}],"day":"01","license":"https://creativecommons.org/licenses/by/4.0/","doi":"10.4230/LIPICS.SOCG.2019.38","file":[{"file_size":559837,"file_id":"6667","date_created":"2019-07-24T06:54:52Z","checksum":"d6d017f8b41291b94d102294fa96ae9c","content_type":"application/pdf","date_updated":"2020-07-14T12:47:35Z","file_name":"2019_LIPICS_Fulek.pdf","access_level":"open_access","creator":"dernst","relation":"main_file"}],"oa":1,"oa_version":"Published Version","year":"2019","month":"06","publication_identifier":{"issn":["1868-8969"],"isbn":["9783959771047"]},"related_material":{"record":[{"relation":"later_version","status":"public","id":"13974"}]},"quality_controlled":"1","conference":{"end_date":"2019-06-21","start_date":"2019-06-18","name":"SoCG 2019: Symposium on Computational Geometry","location":"Portland, OR, United States"},"abstract":[{"lang":"eng","text":"The Tverberg theorem is one of the cornerstones of discrete geometry. It states that, given a set X of at least (d+1)(r-1)+1 points in R^d, one can find a partition X=X_1 cup ... cup X_r of X, such that the convex hulls of the X_i, i=1,...,r, all share a common point. In this paper, we prove a strengthening of this theorem that guarantees a partition which, in addition to the above, has the property that the boundaries of full-dimensional convex hulls have pairwise nonempty intersections. Possible generalizations and algorithmic aspects are also discussed. As a concrete application, we show that any n points in the plane in general position span floor[n/3] vertex-disjoint triangles that are pairwise crossing, meaning that their boundaries have pairwise nonempty intersections; this number is clearly best possible. A previous result of Alvarez-Rebollar et al. guarantees floor[n/6] pairwise crossing triangles. Our result generalizes to a result about simplices in R^d,d >=2."}],"date_updated":"2023-12-13T12:03:35Z","publication_status":"published","intvolume":"       129","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","title":"The crossing Tverberg theorem","external_id":{"arxiv":["1812.04911"]},"date_published":"2019-06-01T00:00:00Z","language":[{"iso":"eng"}],"date_created":"2019-07-17T10:35:04Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}