on subdivisions of oriented cycles in hamiltonian digraphs with small chromatic number

Cohen et al. conjectured that for each oriented cycle $c$, there is a smallest positive integer $f(c)$ such that every $f(c)$-chromatic strong digraph contains a subdivision of $c$. let $c$ be an oriented cycle on $n$ vertices. for the class of hamiltonian digraphs, el joubbeh proved that $f(c)leq 3n$. in this paper, we improve el joubbeh's result by showing that $f(c)leq 2n$ for the class of hamiltonian digraphs.