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 $K_4^-=\{123,124,134\}$, $F_6=\{123,124,345,156\}$ and $\mathcal{F}=\{K_4^-,F_6\}$: for $n\neq 5$ the unique $\mathcal{F}$-free 3-graph of order $n$ and maximum size is the balanced complete tripartite 3-graph $S_3(n)$ (for $n=5$ it is $C_5^{(3)}=\{123,234,345,145,125\}$). This extends an old result of Bollobás that $S_3(n) $ is the unique 3-graph of maximum size with no copy of $K_4^-=\{123,124,134\}$ or $F_5=\{123,124,345\}$.
@article{10_37236_5203,
author = {Adam Sanitt and John Talbot},
title = {An exact {Tur\'an} result for tripartite 3-graphs},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {4},
doi = {10.37236/5203},
zbl = {1323.05076},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5203/}
}
TY - JOUR
AU - Adam Sanitt
AU - John Talbot
TI - An exact Turán result for tripartite 3-graphs
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/5203/
DO - 10.37236/5203
ID - 10_37236_5203
ER -
%0 Journal Article
%A Adam Sanitt
%A John Talbot
%T An exact Turán result for tripartite 3-graphs
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/5203/
%R 10.37236/5203
%F 10_37236_5203
Adam Sanitt; John Talbot. An exact Turán result for tripartite 3-graphs. The electronic journal of combinatorics, Tome 22 (2015) no. 4. doi: 10.37236/5203
