{"type":"conference","extern":1,"publist_id":"4503","date_updated":"2021-01-12T06:57:24Z","abstract":[{"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.","lang":"eng"}],"publication_status":"published","title":"On the rectilinear crossing number of complete graphs","quality_controlled":0,"conference":{"name":"SODA: Symposium on Discrete Algorithms"},"author":[{"orcid":"0000-0002-1494-0568","first_name":"Uli","full_name":"Uli Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner"}],"_id":"2422","main_file_link":[{"url":"http://dl.acm.org/citation.cfm?id=644206","open_access":"0"}],"date_created":"2018-12-11T11:57:34Z","month":"01","citation":{"ieee":"U. Wagner, “On the rectilinear crossing number of complete graphs,” presented at the SODA: Symposium on Discrete Algorithms, 2003, pp. 583–588.","short":"U. Wagner, in:, SIAM, 2003, pp. 583–588.","mla":"Wagner, Uli. <i>On the Rectilinear Crossing Number of Complete Graphs</i>. SIAM, 2003, pp. 583–88.","ama":"Wagner U. On the rectilinear crossing number of complete graphs. In: SIAM; 2003:583-588.","apa":"Wagner, U. (2003). On the rectilinear crossing number of complete graphs (pp. 583–588). Presented at the SODA: Symposium on Discrete Algorithms, SIAM.","ista":"Wagner U. 2003. On the rectilinear crossing number of complete graphs. SODA: Symposium on Discrete Algorithms, 583–588.","chicago":"Wagner, Uli. “On the Rectilinear Crossing Number of Complete Graphs,” 583–88. SIAM, 2003."},"date_published":"2003-01-01T00:00:00Z","day":"01","page":"583 - 588","year":"2003","status":"public","publisher":"SIAM"}