Geodesic
The size-Ramsey number of 3-uniform tight paths
Advances in Combinatorics (2021) Cet article a éte moissonné depuis la source Scholastica

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Given a hypergraph $H$, the size-Ramsey number $\hat{r}_2(H)$ is the smallest integer $m$ such that there exists a graph $G$ with $m$ edges with the property that in any colouring of the edges of $G$ with two colours there is a monochromatic copy of $H$. We prove that the size-Ramsey number of the $3$-uniform tight path on $n$ vertices $P^{(3)}_n$ is linear in $n$, i.e., $\hat{r}_2(P^{(3)}_n) = O(n)$. This answers a question by Dudek, Fleur, Mubayi, and Rödl for $3$-uniform hypergraphs [On the size-Ramsey number of hypergraphs, J. Graph Theory 86 (2016), 417-434], who proved $\hat{r}_2(P^{(3)}_n) = O(n^{3/2} \log^{3/2} n)$.
Publié le : 
@article{ADVC_2021_a4,
     author = {Jie Han and Yoshiharu Kohayakawa and Shoham Letzter and Guilherme Oliveira Mota and Olaf Parczyk},
     title = {The {size-Ramsey} number of 3-uniform tight paths},
     journal = {Advances in Combinatorics},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2021_a4/}
}
TY  - JOUR
AU  - Jie Han
AU  - Yoshiharu Kohayakawa
AU  - Shoham Letzter
AU  - Guilherme Oliveira Mota
AU  - Olaf Parczyk
TI  - The size-Ramsey number of 3-uniform tight paths
JO  - Advances in Combinatorics
PY  - 2021
UR  - http://geodesic.mathdoc.fr/item/ADVC_2021_a4/
LA  - en
ID  - ADVC_2021_a4
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%A Yoshiharu Kohayakawa
%A Shoham Letzter
%A Guilherme Oliveira Mota
%A Olaf Parczyk
%T The size-Ramsey number of 3-uniform tight paths
%J Advances in Combinatorics
%D 2021
%U http://geodesic.mathdoc.fr/item/ADVC_2021_a4/
%G en
%F ADVC_2021_a4
Jie Han; Yoshiharu Kohayakawa; Shoham Letzter; Guilherme Oliveira Mota; Olaf Parczyk. The size-Ramsey number of 3-uniform tight paths. Advances in Combinatorics (2021). http://geodesic.mathdoc.fr/item/ADVC_2021_a4/