The 2-color Ramsey number R(C3 , C3 ) of a 3-uniform loose cycle Cn is asymptotic to 5n/4 as have been recently proved by Haxell, Luczak, Peng, R¨odl, Rucinˆski, Simonovits and Skokan. Here we extend their re- sult to the r-uniform case by showing that the corresponding Ramsey number is asymptotic to (2r−1)n . Partly as a tool, partly as a subject 2r−2 of its own, we also prove that for r ≥ 2, R(kDr , kDr ) = k(2r − 1) − 1 and R(kDr , kDr , kDr ) = 2kr − 2 where kDr is the hypergraph having k disjoint copies of two r-element hyperedges intersecting in two vertices.
, Sárközy, Gábor N.
, Szemerédi, Endre
(2007). The Ramsey number of diamond-matchings and loose cycles in hypergraphs. .
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