In this paper we confirm a special, remaining case of a conjecture of Füredi, Jiang, and Seiver, and determine an exact formula for the Turán number $\mathrm{ex}_3(n; P_3^3)$ of the 3-uniform linear path $P^3_3$ of length 3, valid for all $n$. It coincides with the analogous formula for the 3-uniform triangle $C^3_3$, obtained earlier by Frankl and Füredi for $n\ge 75$ and Csákány and Kahn for all $n$. In view of this coincidence, we also determine a `conditional' Turán number, defined as the maximum number of edges in a $P^3_3$-free 3-uniform hypergraph on $n$ vertices which is not $C^3_3$-free.
@article{10_37236_5320,
author = {Eliza Jackowska and Joanna Polcyn and Andrzej Ruci\'nski},
title = {Tur\'an numbers for 3-uniform linear paths of length 3},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {2},
doi = {10.37236/5320},
zbl = {1336.05142},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5320/}
}
TY - JOUR
AU - Eliza Jackowska
AU - Joanna Polcyn
AU - Andrzej Ruciński
TI - Turán numbers for 3-uniform linear paths of length 3
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/5320/
DO - 10.37236/5320
ID - 10_37236_5320
ER -
%0 Journal Article
%A Eliza Jackowska
%A Joanna Polcyn
%A Andrzej Ruciński
%T Turán numbers for 3-uniform linear paths of length 3
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/5320/
%R 10.37236/5320
%F 10_37236_5320
Eliza Jackowska; Joanna Polcyn; Andrzej Ruciński. Turán numbers for 3-uniform linear paths of length 3. The electronic journal of combinatorics, Tome 23 (2016) no. 2. doi: 10.37236/5320
