  Tropical varieties play an important role in algebraic geometry. The Bergman
complex B(M) and the positive Bergman complex B+(M) of an oriented matroid M
generalize to matroids the notions of the tropical variety and positive
tropical variety associated to a linear ideal. Our main result is that if A is
a Coxeter arrangement of type Phi with corresponding oriented matroid M_Phi,
then B+(M_Phi) is dual to the graph associahedron of type Phi, and B(M_Phi)
equals the nested set complex of A. In addition, we prove that for any
orientable matroid M, one can find |mu(M)| different reorientations of M such
that the corresponding positive Bergman complexes cover B(M), where mu(M)
denotes the Mobius function of the lattice of flats of M.
