A proof for a conjecture of Gyarfas, Lehel, Sarkozy and Schelp on Berge-cycles

It has been conjectured that for any fixed $r\ge 2$ and sufficiently large $n$, there is a monochromatic Hamiltonian Berge-cycle in every $(r-1)$-coloring of the edges of $K_n^r$, the complete $r$-uniform hypergraph on $n$ vertices. In this paper we prove this conjecture.