--- _id: '4103' abstract: - lang: eng text: Let A be an arrangement of n lines in the plane. Suppose F1,…, Fk are faces in the dissection induced by A and that Fi is a t(Fi)-gon. We give asymptotic bounds on the maximal sum ∑i=1kt(Fi) which can be realized by k different faces in an arrangement of n lines. The results improve known bounds for k of higher order than n(1/2). acknowledgement: The second author thanks Gan Gusfield for useful discussion. article_processing_charge: No author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Emo full_name: Welzl, Emo last_name: Welzl citation: ama: Edelsbrunner H, Welzl E. On the maximal number of edges of many faces in an arrangement. Journal of Combinatorial Theory Series A. 1986;41(2):159-166. doi:10.1016/0097-3165(86)90078-6 apa: Edelsbrunner, H., & Welzl, E. (1986). On the maximal number of edges of many faces in an arrangement. Journal of Combinatorial Theory Series A. Elsevier. https://doi.org/10.1016/0097-3165(86)90078-6 chicago: Edelsbrunner, Herbert, and Emo Welzl. “On the Maximal Number of Edges of Many Faces in an Arrangement.” Journal of Combinatorial Theory Series A. Elsevier, 1986. https://doi.org/10.1016/0097-3165(86)90078-6. ieee: H. Edelsbrunner and E. Welzl, “On the maximal number of edges of many faces in an arrangement,” Journal of Combinatorial Theory Series A, vol. 41, no. 2. Elsevier, pp. 159–166, 1986. ista: Edelsbrunner H, Welzl E. 1986. On the maximal number of edges of many faces in an arrangement. Journal of Combinatorial Theory Series A. 41(2), 159–166. mla: Edelsbrunner, Herbert, and Emo Welzl. “On the Maximal Number of Edges of Many Faces in an Arrangement.” Journal of Combinatorial Theory Series A, vol. 41, no. 2, Elsevier, 1986, pp. 159–66, doi:10.1016/0097-3165(86)90078-6. short: H. Edelsbrunner, E. Welzl, Journal of Combinatorial Theory Series A 41 (1986) 159–166. date_created: 2018-12-11T12:06:57Z date_published: 1986-11-01T00:00:00Z date_updated: 2022-02-01T09:46:55Z day: '01' doi: 10.1016/0097-3165(86)90078-6 extern: '1' intvolume: ' 41' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://www.sciencedirect.com/science/article/pii/0097316586900786?via%3Dihub month: '11' oa: 1 oa_version: Published Version page: 159 - 166 publication: Journal of Combinatorial Theory Series A publication_identifier: eissn: - 1096-0899 issn: - 0097-3165 publication_status: published publisher: Elsevier publist_id: '2015' quality_controlled: '1' scopus_import: '1' status: public title: On the maximal number of edges of many faces in an arrangement type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 41 year: '1986' ...