The Ramsey Number of Diamond-Matchings and Loose Cycles in Hypergraphs
The Ramsey Number of Diamond-Matchings and Loose Cycles in Hypergraphs
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 ${(2r-1)n\over 2r-2}$. …