For a finite collection of graphs ℱ, the ℱ-TM-Deletion problem has as input an n-vertex graph G and an integer k and asks whether there exists a set S ⊆ V(G) with |S| ≤ k such that G \ S does not contain any of the graphs in ℱ as a topological minor. We prove that for every such ℱ, ℱ -TM-Deletion is fixed parameter tractable on planar graphs. Our algorithm runs in a 2^𝒪(k2) ⋅ n² time, or, alternatively, in 2^𝒪(k) ⋅ n⁴ time. Our techniques can easily be extended to graphs that are embeddable on any fixed surface.

中文翻译：

---

在平面图中命中拓扑次要模型是固定参数可处理的

对于图 ℱ 的有限集合，ℱ- TM-Deletion问题的输入是一个n顶点图G和一个整数k，并询问是否存在一个集合S ⊆ V(G)和|S| ≤ k使得G \ S不包含 ℱ 中的任何图作为拓扑次要。我们证明对于每个这样的 ℱ，ℱ - TM-Deletion是平面图上易于处理的固定参数。我们的算法运行 2 ^{𝒪( k 2)} ⋅ n ²次，或者 2 ^{𝒪( k )} ⋅ n ^4次时间。我们的技术可以很容易地扩展到可嵌入任何固定表面的图形。