In this paper we study unavoidable sets of types of 3-paths for families of planar graphs with minimum degree at least 2 and a given girth g. A 3-path of type (i,j,k) is a path uvw on three vertices u, v, and w such that the degree of u (resp. v, resp. w) is at most i (resp. j, resp. k). The elements i,j,k are called parameters of the type. The set S of types of paths is unavoidable for a family F of graphs if each graph G from F contains a path of the type from S. An unavoidable set S of types of paths is optimal for the family F if neither any type can be omitted from S, nor any parameter of any type from S can be decreased.
We prove that the set Sg (resp. S′g) is an optimal set of types of 3-paths for the family of plane graphs having δ(G)≥2 and girth g(G)≥g where