Entropy and the clique polynomial

This paper gives a sharp lower bound on the spectral radius (A) of a reciprocal Perron{Frobenius matrix A 2 M2g(Z), and shows in particular that (A) g (3 + p 5)=2. This bound supports conjectures on the minimal entropy of pseudo-Anosov maps. The proof is based on a study of the curve complex of a directed graph.