Geodesic
The Ramsey number of Fano plane versus tight path
József Balogh1 ; Felix Christian Clemen2 ; Jozef Skokan3 ; Adam Zsolt Wagner4
1University of Illinois at Urbana-Champaign and Moscow Institute of Physics and Technology
2University of Illinois at Urbana-Champaign
3London School of Economics
4ETH Zurich
The electronic journal of combinatorics, Tome 27 (2020) no. 1
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

The hypergraph Ramsey number of two $3$-uniform hypergraphs $G$ and $H$, denoted by $R(G,H)$, is the least integer~$N$ such that every red-blue edge-coloring of the complete $3$-uniform hypergraph on $N$ vertices contains a red copy of $G$ or a blue copy of $H$. The Fano plane $\mathbb{F}$ is the unique 3-uniform hypergraph with seven edges on seven vertices in which every pair of vertices is contained in a unique edge. There is a simple construction showing that $R(H,\mathbb{F}) \ge 2(v(H)-1) + 1.$ Hypergraphs $H$ for which the equality holds are called $\mathbb{F}$-good. Conlon asked to determine all $H$ that are $\mathbb{F}$-good.In this short paper we make progress on this problem and prove that the tight path of length $n$ is $\mathbb{F}$-good.
DOI : 10.37236/8374
Classification : 05D10, 05C65, 05C55
Mots-clés : hypergraph Ramsey number

József Balogh  1   ; Felix Christian Clemen  2   ; Jozef Skokan  3   ; Adam Zsolt Wagner  4

1 University of Illinois at Urbana-Champaign and Moscow Institute of Physics and Technology
2 University of Illinois at Urbana-Champaign
3 London School of Economics
4 ETH Zurich 
@article{10_37236_8374,
     author = {J\'ozsef Balogh and Felix Christian Clemen and Jozef Skokan and Adam Zsolt Wagner},
     title = {The {Ramsey} number of {Fano} plane versus tight path},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {1},
     doi = {10.37236/8374},
     zbl = {1435.05200},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8374/}
}
TY  - JOUR
AU  - József Balogh
AU  - Felix Christian Clemen
AU  - Jozef Skokan
AU  - Adam Zsolt Wagner
TI  - The Ramsey number of Fano plane versus tight path
JO  - The electronic journal of combinatorics
PY  - 2020
VL  - 27
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.37236/8374/
DO  - 10.37236/8374
ID  - 10_37236_8374
ER  - 
%0 Journal Article
%A József Balogh
%A Felix Christian Clemen
%A Jozef Skokan
%A Adam Zsolt Wagner
%T The Ramsey number of Fano plane versus tight path
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/8374/
%R 10.37236/8374
%F 10_37236_8374
József Balogh; Felix Christian Clemen; Jozef Skokan; Adam Zsolt Wagner. The Ramsey number of Fano plane versus tight path. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/8374

Cité par Sources :