Tree-like curves and their inflection points

Abstract

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.