{"page":"419 - 430","volume":27,"oa_version":"Submitted Version","title":"A note on the complexity of real algebraic hypersurfaces","publist_id":"3301","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"03","issue":"3","file":[{"file_name":"2011_GraphsCombi_Kerber.pdf","date_updated":"2020-07-14T12:46:08Z","checksum":"a63a1e3e885dcc68f1e3dea68dfbe213","relation":"main_file","date_created":"2020-05-19T16:11:36Z","content_type":"application/pdf","access_level":"open_access","file_id":"7869","creator":"dernst","file_size":143976}],"type":"journal_article","date_published":"2011-03-17T00:00:00Z","language":[{"iso":"eng"}],"date_updated":"2021-01-12T07:42:43Z","has_accepted_license":"1","abstract":[{"lang":"eng","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."}],"department":[{"_id":"HeEd"}],"_id":"3332","doi":"10.1007/s00373-011-1020-7","ddc":["500"],"author":[{"last_name":"Kerber","orcid":"0000-0002-8030-9299","full_name":"Kerber, Michael","first_name":"Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Sagraloff","full_name":"Sagraloff, Michael","first_name":"Michael"}],"intvolume":"        27","publisher":"Springer","scopus_import":1,"citation":{"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.","ista":"Kerber M, Sagraloff M. 2011. A note on the complexity of real algebraic hypersurfaces. Graphs and Combinatorics. 27(3), 419–430.","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>.","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>.","short":"M. Kerber, M. Sagraloff, Graphs and Combinatorics 27 (2011) 419–430.","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>","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>"},"status":"public","date_created":"2018-12-11T12:02:43Z","file_date_updated":"2020-07-14T12:46:08Z","publication":"Graphs and Combinatorics","quality_controlled":"1","article_type":"original","oa":1,"year":"2011","publication_status":"published","day":"17"}