Independence Polynomials and Hypergeometric Series

Let $\Gamma$ be a simple graph and $I_\Gamma(x)$ its multivariate independence polynomial. The main result of this paper is the characterization of chordal graphs as the only $\Gamma$ for which the power series expansion of $I_\Gamma^{-1}(x)$ is Horn hypergeometric.
Comment: v2: 15 pages, added references, improved statement of Theorem 1.2