  A previous work establishing a connection between a quark model, with
relativistic kinematics and a $Y$-confinement plus one gluon exchange, and the
$1/N_c$ expansion mass formula is extended to strange baryons. Both methods
predict values for the SU(3)-breaking mass terms which are in good agreement
with each other. Strange and nonstrange baryons are shown to exhibit Regge
trajectories with an equal slope, but with an intercept depending on the
strangeness. Both approaches agree on the value of the slope and of the
intercept and on the existence of a single good quantum number labeling the
baryons within a given Regge trajectory.
