  We give a criterion when a planar tree-like curve, i.e. a generic immersed
plane curve each double point of which cuts it into two disjoint parts, can be
send by a diffeomorphism of the plane onto a curve with no inflection points.
We also present some upper and lower bounds for the minimal number of
inflection points on such curves unremovable by diffeomorphisms of the plane in
terms of their combinatorics.

Differential Geometry;Differential Geometry