Dorbec–Gyárfás–Sárközy conjecture on monochromatic Hamiltonian tight Berge-cycles

Let $K_n^r$ be the complete $r$-uniform hypergraph on $n$ vertices. For $r\geq t\geq 2$, an $r$-uniform $t$-tight Berge-cycle has a core sequence $v_1,\ldots,v_n$ and distinct edges $e_1,\ldots,e_n$, where $e_i$ contains $v_i,v_{i+1},\ldots,v_{i+t-1}$, with indices taken modulo $n$. It is Hamiltonian when its length is $n$. A $c$-edge coloring assigns one of $c$ colors to every edge.

Dorbec–Gyárfás–Sárközy conjecture. Assume that $c\geq 2$, $2\leq t\leq r$, $c+t\leq r+1$, and $n$ is sufficiently large. Then every $c$-edge coloring of $K_n^r$ contains a monochromatic Hamiltonian $t$-tight Berge-cycle.

The source says that this generalizes the preceding Berge-cycle conjecture and that the proposed bound is best possible if the conjecture is true. It does not provide a resolution of this full assertion, although it proves related results for fewer colors.