The asymptotics of 2-color Ramsey numbers of loose and tight cycles in 3-uniform hypergraphs have been recently determined (, ). We address here the same problem for Berge-cycles and for 3 colors. Our main result is that the 3-color Ramsey number of a 3-uniform Berge cycle of length n is asymptotic to 5n . The result is proved with the Regularity Lemma via the existence of a monochromatic connected matching covering asymptotically 4n/5 vertices in the multicolored 2-shadow graph induced by the coloring of Kn(3) .
, Sárközy, Gábor N.
(2007). The 3-color Ramsey number of a 3-uniform Berge-cycle. .
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