%0 Journal Article
%@ 1077-8926
%A Talbot, JM
%A Sanitt, A
%D 2015
%F discovery:1529897
%I The Electronic Journal of Combinatorics
%J The Electronic Journal of Combinatorics
%N 4
%T An exact Turan result for tripartite 3-graphs
%U https://discovery.ucl.ac.uk/id/eprint/1529897/
%V 22
%X 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}.