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In the Topological Minor Deletion (TM-Deletion) problem input consists of an undirected graph G, a family of undirected graphs F and an integer k. The task is to determine whether G contains a set of vertices S of size at most k, such that the graph G∖ S obtained from G by removing the vertices of S, contains no graph from F as a topological minor. We give an algorithm for TM-Deletionwith running time f(h^,k)· |V(G)|^4. Here h^ is the maximum size of a graph in F and f is a computable functionarXiv:1904.02944v2 fatcat:jqwnhemnerb4nn7blacvnt345u