  The matrix model with a Bethe-tree embedding space (coinciding at large $N$
with the Kazakov-Migdal ``induced QCD'' model \cite{KM}) is investigated. We
further elaborate the Riemann-Hilbert approach of \rf{Mig1} assuming certain
holomorphic properties of the solution. The critical scaling (an edge
singularity of the density) is found to be $\gamma_{str} = -\frac{1}{\pi}
\arcos D$, for $|D|<1$, and $\gamma_{str} = -\frac{1}{\pi} \arcos
\frac{D}{2D-1}$, for $D>1$. Explicit solutions are constructed at
$D=\frac{1}{2}$ and $D=\infty$.
