  In this paper, we classify singular real plane tropical curves by means of
subdivisions of Newton polytopes. First, we introduce signed Bergman fans
(generalizing positive Bergman fans from [AKW06]) that describe real
tropicalizations of real linear spaces ([Tab15]). Then, we establish a duality
of real plane tropical curves and signed regular subdivisions of the Newton
polytope and explore the combinatorics. We define a signed secondary fan that
parametrizes real tropical Laurent polynomials and study the subset providing
singular real plane tropical curves. A cone of the signed secondary fan is of
maximal dimensional type if its corresponding subdivision contains only marked
points ([MMS12a]). These cones parametrize real plane tropical curves. We
classify singular real plane tropical curves of maximal dimensional type.
