[{"main_file_link":[{"url":"http://dl.acm.org/citation.cfm?id=644206"}],"citation":{"chicago":"Wagner, Uli. “On the Rectilinear Crossing Number of Complete Graphs.” In <i>Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms</i>, 583–88. SIAM, 2003. <a href=\"https://doi.org/10.5555/644108.644206\">https://doi.org/10.5555/644108.644206</a>.","mla":"Wagner, Uli. “On the Rectilinear Crossing Number of Complete Graphs.” <i>Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms</i>, SIAM, 2003, pp. 583–88, doi:<a href=\"https://doi.org/10.5555/644108.644206\">10.5555/644108.644206</a>.","ieee":"U. Wagner, “On the rectilinear crossing number of complete graphs,” in <i>Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms</i>, Baltimore, MD, United States, 2003, pp. 583–588.","ista":"Wagner U. 2003. On the rectilinear crossing number of complete graphs. Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms. SODA: Symposium on Discrete Algorithms, 583–588.","ama":"Wagner U. On the rectilinear crossing number of complete graphs. In: <i>Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms</i>. SIAM; 2003:583-588. doi:<a href=\"https://doi.org/10.5555/644108.644206\">10.5555/644108.644206</a>","short":"U. Wagner, in:, Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2003, pp. 583–588.","apa":"Wagner, U. (2003). On the rectilinear crossing number of complete graphs. In <i>Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms</i> (pp. 583–588). Baltimore, MD, United States: SIAM. <a href=\"https://doi.org/10.5555/644108.644206\">https://doi.org/10.5555/644108.644206</a>"},"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","date_updated":"2026-05-28T08:18:32Z","publication_identifier":{"isbn":["9780898715385"]},"extern":"1","author":[{"last_name":"Wagner","full_name":"Wagner, Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli","orcid":"0000-0002-1494-0568"}],"day":"12","quality_controlled":"1","doi":"10.5555/644108.644206","month":"01","OA_type":"closed access","date_created":"2018-12-11T11:57:34Z","publication_status":"published","type":"conference","article_processing_charge":"No","publist_id":"4503","publication":"Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms","_id":"2422","abstract":[{"lang":"eng","text":"We prove a lower bound of 0.3288(4 n) for the rectilinear crossing number cr̄(Kn) of a complete graph on n vertices, or in other words, for the minimum number of convex quadrilaterals in any set of n points in general position in the Euclidean plane. As we see it, the main contribution of this paper is not so much the concrete numerical improvement over earlier bounds, as the novel method of proof, which is not based on bounding cr̄(Kn) for some small n."}],"year":"2003","page":"583 - 588","language":[{"iso":"eng"}],"conference":{"end_date":"2003-01-14","location":"Baltimore, MD, United States","start_date":"2003-01-12","name":"SODA: Symposium on Discrete Algorithms"},"status":"public","title":"On the rectilinear crossing number of complete graphs","publisher":"SIAM","date_published":"2003-01-12T00:00:00Z","oa_version":"None"}]