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A complexity dichotomy for hitting connected minors on bounded treewidth graphs: the chair and the banner draw the boundary [chapter]

Julien Baste, Ignasi Sau, Dimitrios M. Thilikos
2020 Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms  
The above results, together with the lower and upper bounds for planar graphs on at most five vertices given in [5, 6] • 2 Θ(tw) · n O(1) , if H is a contraction of the chair or the banner, and • 2  ...  The crucial role payed by the chair and the bannerin the complexity dichotomy may seem surprising at first sight.  ...  However, in the proof this fact is only used to guarantee that the considered protrusion has treewidth bounded by a function depending only on F .  ... 
doi:10.1137/1.9781611975994.57 dblp:conf/soda/BasteST20 fatcat:ivoy6w7ky5hvlarn2flzspk7ay

Hitting minors on bounded treewidth graphs. IV. An optimal algorithm [article]

Julien Baste, Ignasi Sau, Dimitrios M. Thilikos
2021 arXiv   pre-print
following complexity dichotomy when F = {H} contains a single connected graph H, assuming the Exponential Time Hypothesis: f_H(tw)=2^Θ(tw) if H is a contraction of the chair or the banner, and f_H(tw)  ...  For a fixed finite collection of graphs F, the F-M-DELETION problem asks, given an n-vertex input graph G, for the minimum number of vertices that intersect all minor models in G of the graphs in F. by  ...  The crucial role played by the chair and the banner in the complexity dichotomy may seem surprising at first sight.  ... 
arXiv:1907.04442v2 fatcat:35wobmemrjcgtfro65h6bo4xqe