Outerplanar Obstructions for the Feedback Vertex Set

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