Outerplanar Obstructions for the Feedback Vertex Set

For k⩾1, let Fk be the class containing every graph that contains k vertices meeting all its cycles. The minor-obstruction set for Fk is the set obs(Fk) containing all minor-minimal graph that does not belong to Fk. We denote by Yk the set of all outerplanar graphs in obs(Fk). In this paper, we provide a precise characterization of the class Yk. Then, using the symbolic method, we prove that |Yk|∼α⋅k−5/2⋅ρ−k where α≐0.02602193 and ρ−1≐14.49381704.