@article{discovery1529897, title = {An exact Turan result for tripartite 3-graphs}, number = {4}, year = {2015}, month = {October}, volume = {22}, journal = {The Electronic Journal of Combinatorics}, publisher = {The Electronic Journal of Combinatorics}, url = {http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i4p3/pdf}, 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\}.}, issn = {1077-8926}, author = {Talbot, JM and Sanitt, A} }