  We present the explicit form of the Regge trajectory relations for the triply
heavy bottom-charm baryons, which can be applied to investigate both the
$\lambda$-mode excited states and the $\rho$-mode excited states. We estimate
the masses of the $\lambda$-excited states and the $\rho$-excited states. The
results are in agreement with other theoretical predictions. Both the
$\lambda$-trajectories and the $\rho$-trajectories are discussed. Moreover, the
behaviors of the $\lambda$- and $\rho$-trajectories for various baryons are
discussed. It is shown that both the $\lambda$-trajectories and the
$\rho$-trajectories for baryons are concave downwards in the $(M^2,\,x)$ plane.
The Regge trajectories for the light baryons are approximately linear and
become concave as the masses of the light constituents are considered.
