{"date_created":"2018-12-11T12:02:43Z","month":"03","abstract":[{"text":"Given an algebraic hypersurface O in ℝd, how many simplices are necessary for a simplicial complex isotopic to O? We address this problem and the variant where all vertices of the complex must lie on O. We give asymptotically tight worst-case bounds for algebraic plane curves. Our results gradually improve known bounds in higher dimensions; however, the question for tight bounds remains unsolved for d ≥ 3.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"date_updated":"2021-01-12T07:42:43Z","title":"A note on the complexity of real algebraic hypersurfaces","ddc":["500"],"file_date_updated":"2020-07-14T12:46:08Z","has_accepted_license":"1","file":[{"relation":"main_file","date_updated":"2020-07-14T12:46:08Z","creator":"dernst","date_created":"2020-05-19T16:11:36Z","access_level":"open_access","checksum":"a63a1e3e885dcc68f1e3dea68dfbe213","content_type":"application/pdf","file_size":143976,"file_name":"2011_GraphsCombi_Kerber.pdf","file_id":"7869"}],"publication_status":"published","doi":"10.1007/s00373-011-1020-7","publication":"Graphs and Combinatorics","department":[{"_id":"HeEd"}],"publist_id":"3301","author":[{"last_name":"Kerber","full_name":"Kerber, Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","first_name":"Michael","orcid":"0000-0002-8030-9299"},{"full_name":"Sagraloff, Michael","last_name":"Sagraloff","first_name":"Michael"}],"scopus_import":1,"language":[{"iso":"eng"}],"quality_controlled":"1","year":"2011","intvolume":"        27","page":"419 - 430","day":"17","publisher":"Springer","article_type":"original","citation":{"ama":"Kerber M, Sagraloff M. A note on the complexity of real algebraic hypersurfaces. <i>Graphs and Combinatorics</i>. 2011;27(3):419-430. doi:<a href=\"https://doi.org/10.1007/s00373-011-1020-7\">10.1007/s00373-011-1020-7</a>","ieee":"M. Kerber and M. Sagraloff, “A note on the complexity of real algebraic hypersurfaces,” <i>Graphs and Combinatorics</i>, vol. 27, no. 3. Springer, pp. 419–430, 2011.","mla":"Kerber, Michael, and Michael Sagraloff. “A Note on the Complexity of Real Algebraic Hypersurfaces.” <i>Graphs and Combinatorics</i>, vol. 27, no. 3, Springer, 2011, pp. 419–30, doi:<a href=\"https://doi.org/10.1007/s00373-011-1020-7\">10.1007/s00373-011-1020-7</a>.","ista":"Kerber M, Sagraloff M. 2011. A note on the complexity of real algebraic hypersurfaces. Graphs and Combinatorics. 27(3), 419–430.","short":"M. Kerber, M. Sagraloff, Graphs and Combinatorics 27 (2011) 419–430.","apa":"Kerber, M., &#38; Sagraloff, M. (2011). A note on the complexity of real algebraic hypersurfaces. <i>Graphs and Combinatorics</i>. Springer. <a href=\"https://doi.org/10.1007/s00373-011-1020-7\">https://doi.org/10.1007/s00373-011-1020-7</a>","chicago":"Kerber, Michael, and Michael Sagraloff. “A Note on the Complexity of Real Algebraic Hypersurfaces.” <i>Graphs and Combinatorics</i>. Springer, 2011. <a href=\"https://doi.org/10.1007/s00373-011-1020-7\">https://doi.org/10.1007/s00373-011-1020-7</a>."},"issue":"3","type":"journal_article","article_processing_charge":"No","volume":27,"status":"public","oa_version":"Submitted Version","date_published":"2011-03-17T00:00:00Z","_id":"3332"}