The Ramsey number of diamond-matchings and loose cycles in hypergraphs
The electronic journal of combinatorics, Tome 15 (2008)
The $2$-color Ramsey number $R({\cal{C}}_n^3,{\cal{C}}_n^3)$ of a $3$-uniform loose cycle ${\cal{C}}_n$ is asymptotic to $5n/4$ as has been recently proved by Haxell, Łuczak, Peng, Rödl, Ruciński, Simonovits and Skokan. Here we extend their result to the $r$-uniform case by showing that the corresponding Ramsey number is asymptotic to ${(2r-1)n\over 2r-2}$. Partly as a tool, partly as a subject of its own, we also prove that for $r\ge 2$, $R(kD_r,kD_r)=k(2r-1)-1$ and $R(kD_r,kD_r,kD_r)=2kr-2$ where $kD_r$ is the hypergraph having $k$ disjoint copies of two $r$-element hyperedges intersecting in two vertices.
@article{10_37236_850,
author = {Andr\'as Gy\'arf\'as and G\'abor N. S\'ark\"ozy and Endre Szemer\'edi},
title = {The {Ramsey} number of diamond-matchings and loose cycles in hypergraphs},
journal = {The electronic journal of combinatorics},
year = {2008},
volume = {15},
doi = {10.37236/850},
zbl = {1165.05334},
url = {http://geodesic.mathdoc.fr/articles/10.37236/850/}
}
TY - JOUR AU - András Gyárfás AU - Gábor N. Sárközy AU - Endre Szemerédi TI - The Ramsey number of diamond-matchings and loose cycles in hypergraphs JO - The electronic journal of combinatorics PY - 2008 VL - 15 UR - http://geodesic.mathdoc.fr/articles/10.37236/850/ DO - 10.37236/850 ID - 10_37236_850 ER -
András Gyárfás; Gábor N. Sárközy; Endre Szemerédi. The Ramsey number of diamond-matchings and loose cycles in hypergraphs. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/850
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