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Hitting minors on bounded treewidth graphs. III. Lower bounds
Journal of Computer and System Sciences ( IF 1.129 ) Pub Date : 2019-12-12 , DOI: 10.1016/j.jcss.2019.11.002
Julien Baste; Ignasi Sau; Dimitrios M. Thilikos

For a finite fixed collection of graphs F, the F-M-Deletion problem consists in, given a graph G and an integer k, decide 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 provide lower bounds under the ETH on the smallest function fF such that F-M-Deletion can be solved in time fF(tw)⋅nO(1) on n-vertex graphs, where tw denotes the treewidth of G. We first prove that for any F containing connected graphs of size at least two, fF(tw)=2Ω(tw), even if G is planar. Our main result is that if F contains a single connected graph H that is either P5 or is not a minor of the banner, then fF(tw)=2Ω(tw⋅log⁡tw).
更新日期:2020-01-04

 

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