Geodesic
The Ramsey number of loose triangles and quadrangles in hypergraphs
The electronic journal of combinatorics, Tome 19 (2012) no. 2
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Asymptotic values of hypergraph Ramsey numbers for loose cycles (and paths) were determined recently. Here we determine some of them exactly, for example the 2-color hypergraph Ramsey number of a $k$-uniform loose 3-cycle or 4-cycle: $R(\mathcal{C}^k_3,\mathcal{C}^k_3)=3k-2$ and $R(\mathcal{C}_4^k,\mathcal{C}_4^k)=4k-3$ (for $k\geq 3$). For more than 3-colors we could prove only that $R(\mathcal{C}^3_3,\mathcal{C}^3_3,\mathcal{C}^3_3)=8$. Nevertheless, the $r$-color Ramsey number of triangles for hypergraphs are much smaller than for graphs: for $r\geq 3$, $$r+5\le R(\mathcal{C}_3^3,\mathcal{C}_3^3,\dots,\mathcal{C}_3^3)\le 3r$$
DOI : 10.37236/2346
Classification : 05C55, 05C65, 05C15
Mots-clés : hypergraph Ramsey number, loose cycle, loose path 
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     author = {Andras Gyarfas and Ghaffar Raeisi},
     title = {The {Ramsey} number of loose triangles and quadrangles in hypergraphs},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {2},
     doi = {10.37236/2346},
     zbl = {1243.05161},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2346/}
}
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Andras Gyarfas; Ghaffar Raeisi. The Ramsey number of loose triangles and quadrangles in hypergraphs. The electronic journal of combinatorics, Tome 19 (2012) no. 2. doi: 10.37236/2346

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