{"oa_version":"Published Version","date_published":"1991-03-01T00:00:00Z","oa":1,"abstract":[{"lang":"eng","text":"This paper proves that for every n ≥ 4 there is a convex n-gon such that the vertices of 2n - 7 vertex pairs are one unit of distance apart. This improves the previously best lower bound of ⌊ (5n - 5) 3⌋ given by Erdo{combining double acute accent}s and Moser if n ≥ 17."}],"article_type":"original","publisher":"Elsevier","type":"journal_article","publist_id":"2070","intvolume":"        56","day":"01","page":"312 - 316","issue":"2","article_processing_charge":"No","title":"A lower bound on the number of unit distances between the vertices of a convex polygon","date_created":"2018-12-11T12:06:41Z","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0097-3165"],"eissn":["1096-0899"]},"acknowledgement":"The first author is pleased to acknowledge partial support by the Amoco Fnd. Fat. Dev. Comput. Sci. i-6-44862 and the National Science Foundation under Grant CCR-8714565.","status":"public","month":"03","publication":"Journal of Combinatorial Theory Series A","citation":{"ista":"Edelsbrunner H, Hajnal P. 1991. A lower bound on the number of unit distances between the vertices of a convex polygon. Journal of Combinatorial Theory Series A. 56(2), 312–316.","mla":"Edelsbrunner, Herbert, and Péter Hajnal. “A Lower Bound on the Number of Unit Distances between the Vertices of a Convex Polygon.” <i>Journal of Combinatorial Theory Series A</i>, vol. 56, no. 2, Elsevier, 1991, pp. 312–16, doi:<a href=\"https://doi.org/10.1016/0097-3165(91)90042-F\">10.1016/0097-3165(91)90042-F</a>.","apa":"Edelsbrunner, H., &#38; Hajnal, P. (1991). A lower bound on the number of unit distances between the vertices of a convex polygon. <i>Journal of Combinatorial Theory Series A</i>. Elsevier. <a href=\"https://doi.org/10.1016/0097-3165(91)90042-F\">https://doi.org/10.1016/0097-3165(91)90042-F</a>","ama":"Edelsbrunner H, Hajnal P. A lower bound on the number of unit distances between the vertices of a convex polygon. <i>Journal of Combinatorial Theory Series A</i>. 1991;56(2):312-316. doi:<a href=\"https://doi.org/10.1016/0097-3165(91)90042-F\">10.1016/0097-3165(91)90042-F</a>","chicago":"Edelsbrunner, Herbert, and Péter Hajnal. “A Lower Bound on the Number of Unit Distances between the Vertices of a Convex Polygon.” <i>Journal of Combinatorial Theory Series A</i>. Elsevier, 1991. <a href=\"https://doi.org/10.1016/0097-3165(91)90042-F\">https://doi.org/10.1016/0097-3165(91)90042-F</a>.","short":"H. Edelsbrunner, P. Hajnal, Journal of Combinatorial Theory Series A 56 (1991) 312–316.","ieee":"H. Edelsbrunner and P. Hajnal, “A lower bound on the number of unit distances between the vertices of a convex polygon,” <i>Journal of Combinatorial Theory Series A</i>, vol. 56, no. 2. Elsevier, pp. 312–316, 1991."},"extern":"1","volume":56,"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/009731659190042F?via%3Dihub"}],"publication_status":"published","quality_controlled":"1","doi":"10.1016/0097-3165(91)90042-F","year":"1991","_id":"4056","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_updated":"2022-03-02T09:56:10Z","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Hajnal, Péter","last_name":"Hajnal","first_name":"Péter"}]}