Abstract: Journal of the London Mathematical SocietyVolume 83, Issue 2 p. 389-406 Articles Intersection patterns of curves Jacob Fox, Corresponding Author Jacob Fox [email protected] Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, [email protected] for more papers by this authorJános Pach, János Pach Chair of Combinatorial Geometry, École Polytechnique Fédérale de Lausanne, Station 8, CH-1015 Lausanne, Switzerland, and, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA, [email protected] for more papers by this authorCsaba D. Tóth, Csaba D. Tóth Department of Mathematics, University of Calgary, 2500 University Drive NW, Calgary, AB, Canada T2P 1N4, [email protected] for more papers by this author Jacob Fox, Corresponding Author Jacob Fox [email protected] Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, [email protected] for more papers by this authorJános Pach, János Pach Chair of Combinatorial Geometry, École Polytechnique Fédérale de Lausanne, Station 8, CH-1015 Lausanne, Switzerland, and, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA, [email protected] for more papers by this authorCsaba D. Tóth, Csaba D. Tóth Department of Mathematics, University of Calgary, 2500 University Drive NW, Calgary, AB, Canada T2P 1N4, [email protected] for more papers by this author First published: 06 February 2011 https://doi.org/10.1112/jlms/jdq087Citations: 20 2000 Mathematics Subject Classification 05D10, 05C62 (primary), 05C35, 06A07 (secondary). The first author was supported by an NSF Graduate Research Fellowship and a Princeton Centennial Fellowship. The second author was supported by NSF Grant CCF-05-14079, by OTKA, by Swiss National Science Foundation Grant 200021-125287/1, and by the Bernoulli Interdisciplinary Center at EPFL. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract We prove that for every k ∈ ℕ there is a constant ck > 0 with the following property. Every set of n > 1 continuous curves in the plane, any pair of which intersect in at most k points, has two disjoint subsets A and B, each of size at least ckn, such that either every curve in A intersects all curves in B, or no curve in A intersects any curve in B. This statement does not remain true if we drop the condition on the number of intersection points per pair. Citing Literature Volume83, Issue2April 2011Pages 389-406 RelatedInformation