The anti-Ramsey problem was introduced by Erd\H{ o}s, Simonovits and S\'{ o}s in 1970s. The anti-Ramsey number of a hypergraph $\mathcal{ H}$, $ar(n,s, \mathcal{ H})$, is the smallest integer $c$ such that in any coloring of the edges of the $s$-uniform complete hypergraph on $n$ vertices with exactly $c$ colors, there is a copy of $\mathcal{ H}$ whose edges have distinct colors. In this paper, we determine the anti-Ramsey numbers of linear paths and loose paths in hypergraphs for sufficiently large $n$, and give bounds for the anti-Ramsey numbers of Berge paths. Similar exact anti-Ramsey numbers are obtained for linear/loose cycles, and bounds are obtained for Berge cycles. Our main tools are path extension technique and stability results on hypergraph Tur\'{ a}n problems of paths and cycles.
Categories: math.CO