  We study octet-octet baryon ($J^P = {\textstyle \frac12}^+$) contact
interactions in SU(3) chiral effective field theory by using large-$N_c$
operator analysis. Applying the $1/N_c$ expansion of the Hartee Hamiltonian, we
find 15 operators in the octet-octet baryon potential where 4 operators for
leading order (LO) and 11 for and net-to-next-to-leading order (NNLO). The
large-$N_c$ operator analysis of octet-octet baryon matrix elements reduces the
number of free parameters from 15 to 6 at LO of the $1/N_c$ expansion. The
application of large-$N_c$ sum rules to the J\"{u}lich model of hyperon-nucleon
(YN) interactions at the LO of the chiral expansion reduces the model
parameters to 3 from 5 at the LO of $1/N_c$ expansion. We find that the values
of LECs fitted to YN scattering data in Ref. \cite{Li:2016paq} in the
relativistic covariant ChEFT (EG) approach is more consistent with the
predictions of large-$N_c$ than in the heavy baryon (HB) formalism approach.
