  Using the Callan-Klebanov bound state model for hyperons simulated on crystal
lattice to describe strange baryonic matter, we argue that to ${\cal O} (1)$ in
the large $N_c$ counting to which the theory is robust, hyperons can figure
only when -- or after -- kaons condense in compact-star matter. We also discuss
how the skyrmion-half-skyrmion topological transition affects the equation of
state (EoS) of dense baryonic matter. The observations made in this note open
wide the issue of how to theoretically access the EoS of compact stars.
