  We establish the following fundamentals about Lagrangian models of
meson-baryon interactions in the large-$N_{c}$ limit: 1. Calculating the
leading-order contribution to $1$-meson/$2$-baryon Green's functions in the
$1/N_c$ expansion involves summing an infinite class of divergent Feynman
diagrams. So long as the bare Lagrangian properly obeys all large-$N_c$
selection rules, this all-loops resummation is accomplished exactly by solving
coupled classical field equations with a short-distance cutoff. 2. The only
effect of the resummation is to renormalize the bare Yukawa couplings, baryon
masses and hyperfine baryon mass splittings of the model. 3. In the process,
the large-$N_{c}$ renormalization group flow of these bare parameters is
completely determined. We conjecture that variants of the Skyrme model emerge
as UV fixed points of such flows.
