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We investigate the charm hadron production in relativistic heavy-ioncollisions with the quark combination model. The $p_{T}$ dependencies of thecharm baryon to meson ratios such as$\frac{\Lambda_{c}+\bar{\Lambda}_{c}}{D^{0}+\bar{D}^{0}}$,$\frac{\Lambda_{c}+\bar{\Lambda}_{c}}{D^{+}+D^{-}}$ and$\frac{\Lambda_{c}+\bar{\Lambda}_{c}}{D_{s}^{+}+D_{s}^{-}}$ in Au+Au collisionsat 200 GeV are obtained. The charm baryon enhancement in the intermediate$p_{T}$ range is very prominent, which further, together with the strangenessenhancement, affect the charm hadron ratios and lead to a $\sim17%$ largercharm cross-section given by PHENIX. The dependencies of the charm hadronratios on energy, centrality, and other parameters are also investigated.Predictions of the charm hadron ratios for the upgrade of RHIC and for LHC arepresented.

Charm hadron production in relativistic heavy ion collisions within a quark combination model