Abstract: Journal of the London Mathematical SocietyVolume 68, Issue 1 p. 37-51 Notes and Papers Intersecting Families of Separated Sets John Talbot, John Talbot Merton College, University of Oxford, Oxford, [email protected]Search for more papers by this author John Talbot, John Talbot Merton College, University of Oxford, Oxford, [email protected]Search for more papers by this author First published: 23 December 2016 https://doi.org/10.1112/S0024610703004356Citations: 27AboutPDF 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 onEmailFacebookTwitterLinkedInRedditWechat Abstract A set A ⊆ {1,2,…,n} is said to be k-separated if, when considered on the circle, any two elements of A are separated by a gap of size at least k. A conjecture due to Holroyd and Johnson that an analogue of the Erdős–Ko–Rado theorem holds for k-separated sets is proved. In particular, the result holds for the vertex-critical subgraph of the Kneser graph identified by Schrijver, the collection of separated sets. A version of the Erdős–Ko–Rado theorem for weighted k-separated sets is also given. Citing Literature Volume68, Issue1August 2003Pages 37-51 RelatedInformation