The Ramsey Number for 4-Uniform Tight Cycles

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