{"abstract":[{"lang":"eng","text":"We show that the maximum number of edges bounding m faces in an arrangement of n line segments in the plane is O(m2/3n2/3+nα(n)+nlog m). This improves a previous upper bound of Edelsbrunner et al. [5] and almost matches the best known lower bound which is Ω(m2/3n2/3+nα(n)). In addition, we show that the number of edges bounding any m faces in an arrangement of n line segments with a total of t intersecting pairs is O(m2/3t1/3+nα(t/n)+nmin{log m,log t/n}), almost matching the lower bound of Ω(m2/3t1/3+nα(t/n)) demonstrated in this paper."}],"publication_status":"published","publication":"Combinatorica","author":[{"last_name":"Aronov","full_name":"Aronov, Boris","first_name":"Boris"},{"orcid":"0000-0002-9823-6833","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"},{"first_name":"Leonidas","full_name":"Guibas, Leonidas","last_name":"Guibas"},{"full_name":"Sharir, Micha","first_name":"Micha","last_name":"Sharir"}],"doi":"10.1007/BF01285815","_id":"4053","publication_identifier":{"issn":["0209-9683"]},"type":"journal_article","extern":"1","volume":12,"date_updated":"2022-03-15T15:44:26Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"261 - 274","status":"public","date_created":"2018-12-11T12:06:40Z","month":"09","citation":{"mla":"Aronov, Boris, et al. “The Number of Edges of Many Faces in a Line Segment Arrangement.” <i>Combinatorica</i>, vol. 12, no. 3, Springer, 1992, pp. 261–74, doi:<a href=\"https://doi.org/10.1007/BF01285815\">10.1007/BF01285815</a>.","ama":"Aronov B, Edelsbrunner H, Guibas L, Sharir M. The number of edges of many faces in a line segment arrangement. <i>Combinatorica</i>. 1992;12(3):261-274. doi:<a href=\"https://doi.org/10.1007/BF01285815\">10.1007/BF01285815</a>","short":"B. Aronov, H. Edelsbrunner, L. Guibas, M. Sharir, Combinatorica 12 (1992) 261–274.","ieee":"B. Aronov, H. Edelsbrunner, L. Guibas, and M. Sharir, “The number of edges of many faces in a line segment arrangement,” <i>Combinatorica</i>, vol. 12, no. 3. Springer, pp. 261–274, 1992.","chicago":"Aronov, Boris, Herbert Edelsbrunner, Leonidas Guibas, and Micha Sharir. “The Number of Edges of Many Faces in a Line Segment Arrangement.” <i>Combinatorica</i>. Springer, 1992. <a href=\"https://doi.org/10.1007/BF01285815\">https://doi.org/10.1007/BF01285815</a>.","ista":"Aronov B, Edelsbrunner H, Guibas L, Sharir M. 1992. The number of edges of many faces in a line segment arrangement. Combinatorica. 12(3), 261–274.","apa":"Aronov, B., Edelsbrunner, H., Guibas, L., &#38; Sharir, M. (1992). The number of edges of many faces in a line segment arrangement. <i>Combinatorica</i>. Springer. <a href=\"https://doi.org/10.1007/BF01285815\">https://doi.org/10.1007/BF01285815</a>"},"article_processing_charge":"No","oa_version":"None","issue":"3","title":"The number of edges of many faces in a line segment arrangement","scopus_import":"1","quality_controlled":"1","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF01285815"}],"language":[{"iso":"eng"}],"intvolume":"        12","publist_id":"2074","date_published":"1992-09-01T00:00:00Z","day":"01","year":"1992","publisher":"Springer","article_type":"original"}