%V 22
%D 2015
%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}.
%A JM Talbot
%A A Sanitt
%T An exact Turan result for tripartite 3-graphs
%J The Electronic Journal of Combinatorics
%N 4
%I The Electronic Journal of Combinatorics
%L discovery1529897