eprintid: 1529897 rev_number: 19 eprint_status: archive userid: 608 dir: disk0/01/52/98/97 datestamp: 2017-03-16 15:21:09 lastmod: 2020-02-12 18:14:19 status_changed: 2017-03-16 15:21:09 type: article metadata_visibility: show creators_name: Talbot, JM creators_name: Sanitt, A title: An exact Turan result for tripartite 3-graphs ispublished: pub divisions: UCL divisions: A01 divisions: B04 divisions: C06 divisions: F59 abstract: Mantel’s theorem says that among all triangle-free graphs of a given order the balanced complete bipartite graph is the unique graph of maximum size. We prove an analogue of this result for 3-graphs. Let K− 4 = {123, 124, 134}, F6 = {123, 124, 345, 156} and F = {K− 4 , F6}: for n 6= 5 the unique F-free 3-graph of order n and maximum size is the balanced complete tripartite 3-graph S3(n) (for n = 5 it is C (3) 5 = {123, 234, 345, 145, 125}). This extends an old result of Bollob´as that S3(n) is the unique 3-graph of maximum size with no copy of K− 4 = {123, 124, 134} or F5 = {123, 124, 345}. date: 2015-10-16 date_type: published publisher: The Electronic Journal of Combinatorics official_url: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i4p3/pdf oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green article_type_text: Article verified: verified_manual elements_id: 1193359 lyricists_name: Sanitt, Adam lyricists_name: Talbot, John lyricists_id: SANIT53 lyricists_id: JMTAL98 actors_name: Cassidy, David actors_name: Laslett, David actors_id: DBCAS57 actors_id: DLASL34 actors_role: owner actors_role: impersonator full_text_status: public publication: The Electronic Journal of Combinatorics volume: 22 number: 4 article_number: 4.3 issn: 1077-8926 citation: Talbot, JM; Sanitt, A; (2015) An exact Turan result for tripartite 3-graphs. The Electronic Journal of Combinatorics , 22 (4) , Article 4.3. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/1529897/1/Sanitt_5203-15246-2-PB.pdf