  We consider the Steiner tree problem in hyperbolic geometry in the context of
the AdS/CFT duality between large-$c$ conformal blocks on the boundary and
particle motions in the bulk. The Steiner trees are weighted graphs on the
Poincare disk with a number of endpoints and trivalent vertices connected to
each other by edges in such a way that an overall length is minimum. We specify
a particular class of Steiner trees that we call holographic. Their
characteristic property is that a holographic Steiner tree with $N$ endpoints
can be inscribed into an $N$-gon with $N-1$ ideal vertices. The holographic
Steiner trees are dual to large-$c$ conformal blocks. Particular examples of
$N=2,3,4$ Steiner trees as well as their dual conformal blocks are explicitly
calculated. We discuss geometric properties of the holographic Steiner trees
and their realization in CFT terms. It is shown that connectivity and cuts of
the Steiner trees encode the factorization properties of large-$c$ conformal
blocks.
