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Séminaire Algo - Julien Baste
Séminaire Algo - Julien Baste
9-oct.-2018 14:00
Il y a: 8 days

Julien Baste

Hitting minors on bounded treewidth graphs

Bâtiment Lavoisier, salle 27

For a fixed collection of graphs F, the F-DELETION problem consists in, given a graph G and an integer k, decide whether there exists S, subset of V(G), with |S| <= k such that G-S does not contain any of the graphs in F as a minor. This NP-hard problem is a generalization of some well known graph problems as VERTEX COVER (F={K_2}), FEEDBACK VERTEX SET (F={K_3}), or VERTEX PLANARIZATION (F={K_5,K_{3,3}}). We are interested in its parameterized complexity when the parameter is the treewidth of G, denoted by tw. Namely, the objective is to determine, for a fixed F, the (asymptotically) smallest function f_F: N -> N such that F-DELETION can be solved in time f_F(tw)*n^{O(1)} on n-vertex graphs. In this talk we will provide the basic definitions of parameterized complexity, motivate the problem, and then, review some of the lower and upper bounds on the function f_F for several instantiations of F. The presented results are joint work with Ignasi Sau and Dimitrios Thilikos and can be found in [arXiv:1704.07284].

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