Hitting minors on bounded treewidth graphs. I. General upper bounds [article]

Julien Baste, Ignasi Sau, Dimitrios M. Thilikos
2021 arXiv   pre-print
For a finite collection of graphs F, the F-M-DELETION problem consists in, given a graph G and an integer k, deciding whether there exists S ⊆ V(G) with |S| ≤ k such that G ∖ S does not contain any of the graphs in F as a minor. We are interested in the parameterized complexity of F-M-DELETION when the parameter is the treewidth of G, denoted by tw. Our objective is to determine, for a fixed F, the smallest function f_ F such that F-M-DELETION can be solved in time f_ F(tw) · n^O(1) on n-vertex
more » ... graphs. We prove that f_ F(tw) = 2^2^O(tw ·log tw) for every collection F, that f_ F(tw) = 2^O(tw ·log tw) if F contains a planar graph, and that f_ F(tw) = 2^O(tw) if in addition the input graph G is planar or embedded in a surface. We also consider the version of the problem where the graphs in F are forbidden as topological minors, called F-TM-DELETION. We prove similar results for this problem, except that in the last two algorithms, instead of requiring F to contain a planar graph, we need it to contain a subcubic planar graph. This is the first of a series of articles on this topic.
arXiv:1704.07284v5 fatcat:thcx7bx27vephlv454jsdciauy