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A $k$-uniform tight cycle is a $k$-graph with a cyclic ordering of itsvertices such that its edges are precisely the sets of $k$ consecutive verticesin that ordering. A $k$-uniform tight path is a $k$-graph obtained by deletinga vertex from a $k$-uniform tight cycle. We prove that the Ramsey number forthe $4$-uniform tight cycle on $4n$ vertices is $(5 +o(1))n$. This isasymptotically tight. This result also implies that the Ramsey number for the$4$-uniform tight path on $n$ vertices is $(5/4 + o(1))n$.

The Ramsey number for 4-uniform tight cycles