Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 2 2026 06 01 On subdivisions of oriented cycles in Hamiltonian digraphs with small chromatic number 307 314 14813 10.22049/cco.2024.29517.2036 EN Salman Ghazal Department of Mathematics and Physics, Lebanese International University, LIU, Beirut, Lebanon Department of Mathematics and Physics, The International University of Beirut, BIU, Beirut, Lebanon Department of Mathematics, Faculty of Sciences I, Lebanese University, Beirut, Lebanon Sara Tfaili Department of Mathematics and Physics, Lebanese International University, LIU, Beirut, Lebanon Department of Mathematics and Physics, The International University of Beirut, BIU, Beirut, Lebanon 0000-0003-0906-3457 Journal Article 2024 03 08 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. https://comb-opt.azaruniv.ac.ir/article_14813_079a99ca1446fbf86ac1dca81ee4b632.pdf