Browsing by Author "Diner, Oznur Yasar"

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Citation Count: 1
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
Citation Count: 0
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.
Citation Count: 0
Four-searchable biconnected outerplanar graphs
(Elsevier, 2022) Diner, Oznur Yasar; Dyer, Danny; Yang, Boting
This paper deals with constructing obstruction sets for two subclasses of 4-searchable graphs. We first characterize the 4-searchable biconnected outerplanar graphs by listing all graphs that cannot be their minors; we then give a constructive characterization of such graphs. We also characterize the 4-searchable biconnected generalized wheel graphs by listing all graphs that cannot be their minors. Crown Copyright (C) 2021 Published by Elsevier B.V. All rights reserved.
List Coloring Based Algorithm for the Futoshiki Puzzle
(Ramazan Yaman, 2024) Sen, Banu Baklan; Diner, Oznur Yasar
Given a graph G = ( V, E ) and a list of available colors L ( v ) for each vertex v is an element of V , where L ( v ) subset of {1,2, . . . , k }, LIST k-COLORING refers to the problem of assigning colors to the vertices of G so that each vertex receives a color from its own list and no two neighboring vertices receive the same color. The decision version of the problem, LIST k-COLORING, is NP-complete even for bipartite graphs. As an application of list coloring problem we are interested in the Futoshiki Problem. Futoshiki is an NP-complete Latin Square Completion Type Puzzle. Considering Futoshiki puzzle as a constraint satisfaction problem, we first give a list coloring based algorithm for it which is efficient for small boards of fixed size. To thoroughly investigate the efficiency of our algorithm in comparison with a proposed backtracking-based algorithm, we conducted a substantial number of computational experiments at different difficulty levels, considering varying numbers of inequality constraints and given values. Our results from the extensive range of experiments indicate that the list coloring-based algorithm is much more efficient.
Citation Count: 0
The multicolored graph realization problem
(Elsevier, 2024) Diaz, Josep; Diner, Oznur Yasar; Serna, Maria; Serra, Oriol
We introduce the multicolored graph realization problem (MGR). The input to this problem is a colored graph ( G , phi ), i.e., a graph G together with a coloring phi on its vertices. We associate each colored graph ( G , phi ) with a cluster graph ( G phi ) in which, after collapsing all vertices with the same color to a node, we remove multiple edges and self -loops. A set of vertices S is multicolored when S has exactly one vertex from each color class. The MGR problem is to decide whether there is a multicolored set S so that, after identifying each vertex in S with its color class, G [ S ] coincides with G phi . The MGR problem is related to the well-known class of generalized network problems, most of which are NP -hard, like the generalized Minimum Spanning Tree problem. The MGR is a generalization of the multicolored clique problem, which is known to be W [ 1 ] -hard when parameterized by the number of colors. Thus, MGR remains W [ 1 ] - hard, when parameterized by the size of the cluster graph. These results imply that the MGR problem is W [ 1 ] -hard when parameterized by any graph parameter on G phi , among which lies treewidth. Consequently, we look at the instances of the problem in which both the number of color classes and the treewidth of G phi are unbounded. We consider three natural such graph classes: chordal graphs, convex bipartite graphs and 2 -dimensional grid graphs. We show that MGR is NP -complete when G phi is either chordal, biconvex bipartite, complete bipartite or a 2 -dimensional grid. Our reductions show that the problem remains hard even when the maximum number of vertices in a color class is 3. In the case of the grid, the hardness holds even for graphs with bounded degree. We provide a complexity dichotomy with respect to cluster size. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Citation Count: 0
On minimum vertex bisection of random d-regular graphs
(Academic Press inc Elsevier Science, 2024) Diaz, Josep; Diner, Oznur Yasar; Serna, Maria; Serra, Oriol
Minimum vertex bisection is a graph partitioning problem in which the aim is to find a partition of the vertices into two equal parts that minimizes the number of vertices in one partition set that have a neighbor in the other set. In this work we are interested in providing asymptotically almost surely upper bounds on the minimum vertex bisection of random d -regular graphs, for constant values of d . Our approach is based on analyzing a greedy algorithm by using the differential equation method. In this way, we obtain the first known non -trivial upper bounds for the vertex bisection number in random regular graphs. The numerical approximations of these theoretical bounds are compared with the emprical ones, and with the lower bounds from Kolesnik and Wormald (2014) [30]. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).