## Subexponential Parameterized Algorithms on Graphs of Bounded Genus and H-Minor-Free Graphs (2003)

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@MISC{Demaine03subexponentialparameterized,

author = {Erik D. Demaine and Fedor V. Fomin and MohammadTaghi Hajiaghayi and Dimitrios M. Thilikos},

title = {Subexponential Parameterized Algorithms on Graphs of Bounded Genus and H-Minor-Free Graphs},

year = {2003}

}

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### Abstract

We introduce a new framework for designing fixed-parameter algorithms with subexponential running time---2 . Our results apply to a broad family of graph problems, called bidimensional problems, which includes many domination and covering problems such as vertex cover, feedback vertex set, minimum maximal matching, dominating set, edge dominating set, clique-transversal set, and many others restricted to bounded genus graphs. Furthermore, it is fairly straightforward to prove that a problem is bidimensional. In particular, our framework includes as special cases all previously known problems to have such subexponential algorithms. Previously, these algorithms applied to planar graphs, single-crossing-minor-free graphs, and/or map graphs; we extend these results to apply to bounded-genus graphs as well. In a parallel development of combinatorial results, we establish an upper bound on the treewidth (or branchwidth) of a bounded-genus graph that excludes some planar graph H as a minor. This bound depends linearly on the size (H)| of the excluded graph H and the genus g(G) of the graph G, and applies and extends the graph-minors work of Robertson and Seymour. Building on these results...