Browsing by Author "Thilikos, Dimitrios M."

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    Block Elimination Distance
    (Springer Japan Kk, 2022) Diner, Oznur Yasar; Giannopoulou, Archontia C.; Stamoulis, Giannos; Thilikos, Dimitrios M.
    We introduce the parameter of block elimination distance as a measure of how close a graph is to some particular graph class. Formally, given a graph class g, the class B(G) contains all graphs whose blocks belong to G and the class A(G) contains all graphs where the removal of a vertex creates a graph in G. Given a hereditary graph class G, we recursively define G((k)) so that G((0)) = B(G) and, if k >= 1 G((k)) B(A(G((k-1))) ) N We show that, for every nontrivial hereditary class g, the problem of deciding whether G is an element of G((k)) is NP-complete. We focus on the case where G is minor-closed and we study the minor obstruction set of G((k)) i.e., the minor-minimal graphs not in G((k)). We prove that the size of the obstructions of G((k)) is upper bounded by some explicit function ofk and the maximum size of a minor obstruction of G. This implies that the problem of deciding whether G is an element of G((k)) is constructively fixed parameter tractable, when parameterized by k. Finally, we give two graph operations that generate members of G((k)) from members of G((k -1)) and we prove that this set of operations is complete for the class O of outerplanar graphs.Please check and confirm if the authors Given and Family names have been correctly identified for author znur YaYar Diner. All authors names have been identified conectly. Please confirm if the corresponding author is correctly identified. Amend if necessary.This is correct
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    Block Elimination Distance
    (Springer international Publishing Ag, 2021) Diner, Oznur Yasar; Giannopoulou, Archontia C.; Stamoulis, Giannos; Thilikos, Dimitrios M.
    We introduce the parameter of block elimination distance as a measure of how close a graph is to some particular graph class. Formally, given a graph class G, the class B(G) contains all graphs whose blocks belong to G and the class A(G) contains all graphs where the removal of a vertex creates a graph in G. Given a hereditary graph class G, we recursively define G((k)) so that G((0)) = B(G) and, if k >= 1, G((k)) = B(A(G((k-1)))). The block elimination distance of a graph G to a graph class G is the minimum k such that G is an element of G((k)) and can be seen as an analog of the elimination distance parameter, defined in [J. Bulian & A. Dawar. Algorithmica, 75(2):363-382, 2016], with the difference that connectivity is now replaced by biconnectivity. We show that, for every non-trivial hereditary class G, the problem of deciding whether G. G(k) is NPcomplete. We focus on the case where G is minor-closed and we study the minor obstruction set of G((k)) i.e., the minor-minimal graphs not in G((k)). We prove that the size of the obstructions of G((k)) is upper bounded by some explicit function of k and the maximum size of a minor obstruction of G. This implies that the problem of deciding whether G is an element of G((k)) is constructively fixed parameter tractable, when parameterized by k. Our results are based on a structural characterization of the obstructions of B(G), relatively to the obstructions of G. Finally, we give two graph operations that generate members of G((k)) from members of G((k-1)) and we prove that this set of operations is complete for the class O of outerplanar graphs. This yields the identification of all members O boolean AND G((k)), for every k is an element of N and every non-trivial minor-closed graph class G.