Let $H$ and $F$ be hypergraphs. We say $H$ {\em contains $F$ as a trace} if there exists some set $S \subseteq V(H)$ such that $H|_S:=\{E\cap S: E \in E(H)\}$ contains a subhypergraph isomorphic to $F$. In this paper we give an upper bound on the number of edges in a $3$-uniform hypergraph that does not contain $K_{2,t}$ as a trace when $t$ is large. In particular, we show that $$\lim_{t\to \infty}\lim_{n\to \infty} \frac{\mathrm{ex}(n, \mathrm{Tr}_3(K_{2,t}))}{t^{3/2}n^{3/2}} = \frac{1}{6}.$$ Moreover, we show $\frac{1}{2} n^{3/2} + o(n^{3/2}) \leqslant \mathrm{ex}(n, \mathrm{Tr}_3(C_4)) \leqslant \frac{5}{6} n^{3/2} + o(n^{3/2})$.
@article{10_37236_9760,
author = {Ruth Luo and Sam Spiro},
title = {Forbidding {\(K_{2,t}\)} traces in triple systems},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {2},
doi = {10.37236/9760},
zbl = {1461.05234},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9760/}
}
TY - JOUR
AU - Ruth Luo
AU - Sam Spiro
TI - Forbidding \(K_{2,t}\) traces in triple systems
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/9760/
DO - 10.37236/9760
ID - 10_37236_9760
ER -
%0 Journal Article
%A Ruth Luo
%A Sam Spiro
%T Forbidding \(K_{2,t}\) traces in triple systems
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/9760/
%R 10.37236/9760
%F 10_37236_9760
Ruth Luo; Sam Spiro. Forbidding \(K_{2,t}\) traces in triple systems. The electronic journal of combinatorics, Tome 28 (2021) no. 2. doi: 10.37236/9760
