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Hitting forbidden subgraphs in graphs of bounded treewidth
"... We study the complexity of a generic hitting problem HSubgraph Hitting, where given a fixed pattern graph H and an input graph G, we seek for the minimum size of a set X ⊆ V (G) that hits all subgraphs of G isomorphic to H. In the colorful variant of the problem, each vertex of G is precolored wi ..."
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We study the complexity of a generic hitting problem HSubgraph Hitting, where given a fixed pattern graph H and an input graph G, we seek for the minimum size of a set X ⊆ V (G) that hits all subgraphs of G isomorphic to H. In the colorful variant of the problem, each vertex of G is precolored
THE COPS AND ROBBER GAME ON GRAPHS WITH FORBIDDEN (INDUCED) SUBGRAPHS
, 2008
"... The twoplayer, complete information game of Cops and Robber is played on undirected finite graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if, after a move, a cop and the robber are on the same vertex. The minimum number of cop ..."
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Cited by 5 (0 self)
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of cops needed to catch the robber on a graph is called the cop number of that graph. In this paper, we study the cop number in the classes of graphs defined by forbidding one or more graphs as either subgraphs or induced subgraphs. In the case of a single forbidden graph we completely characterize (for
Uniform Kernelization Complexity of Hitting Forbidden Minors
"... The FMinorFree Deletion problem asks, for a fixed set F and an input consisting of a graph G and integer k, whether k vertices can be removed from G such that the resulting graph does not contain any member of F as a minor. It generalizes classic graph problems such as Vertex Cover and Feedback Ve ..."
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polynomial, i.e., of the form f(F) ·kc for some universal constant c that does not depend on F. Our results in this paper are twofold. 1. We prove that not all Planar FMinorFree Deletion problems have uniformly polynomial kernels (unless NP ⊆ coNP/poly). Since a graph class has bounded treewidth
Forbidden subgraph colorings and the oriented chromatic number
 Proc. 20th Int. Workshop on Combinatorial Algorithms, IWOCA’09, Lecture Notes in Comput. Sci. 5874
, 2009
"... Abstract. We present an improved upper bound of O(d1+ 1 m−1) for the (2,F)subgraph chromatic number χ2,F (G) of any graph G of maximum degree d. Here, m denotes the minimum number of edges in any member of F. This bound is tight up to a (log d)1/(m−1) multiplicative factor and improves the previous ..."
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Cited by 5 (2 self)
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the previous bound presented in [1]. We also obtain a relationship connecting the oriented chromatic number χo(G) of graphs and the (j,F)subgraph chromatic numbers χj,F (G) introduced and studied in [1]. In particular, we relate oriented chromatic number and the (2, r)treewidth chromatic number and show
Induced Subgraphs of Bounded Degree and Bounded Treewidth
"... We prove that for all 0 ≤ t ≤ k and d ≥ 2k, every graph G with treewidth at most k has a ‘large ’ induced subgraph H, where H has treewidth at most t and every vertex in H has degree at most d in G. The order of H depends on t, k, d, and the order of G. With t = k, we obtain large sets of bounded de ..."
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Cited by 1 (0 self)
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We prove that for all 0 ≤ t ≤ k and d ≥ 2k, every graph G with treewidth at most k has a ‘large ’ induced subgraph H, where H has treewidth at most t and every vertex in H has degree at most d in G. The order of H depends on t, k, d, and the order of G. With t = k, we obtain large sets of bounded
Subgraph Isomorphism, logBounded Fragmentation, and Graphs of (Locally) Bounded Treewidth
 in Proc. the 27th International Symposium on Mathematical Foundations of Computer Science
, 2002
"... The subgraph isomorphism problem, that of nding a copy of one graph in another, has proved to be intractable except when certain restrictions are placed on the inputs. In this paper, we introduce a new property for graphs (a generalization on bounded degree) and extend the known classes of input ..."
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Cited by 13 (4 self)
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time algorithm for nding a subgraph of H isomorphic to a graph G when G is a logbounded fragmentation graph and H has bounded treewidth; these results are extended to handle graphs of locally bounded treewidth (a generalization of treewidth) when G is a logbounded fragmentation graph and has constant
Diameter and Treewidth in MinorClosed Graph Families
, 1999
"... It is known that any planar graph with diameter D has treewidth O(D), and this fact has been used as the basis for several planar graph algorithms. We investigate the extent to which similar relations hold in other graph families. We show that treewidth is bounded by a function of the diameter in a ..."
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Cited by 111 (2 self)
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It is known that any planar graph with diameter D has treewidth O(D), and this fact has been used as the basis for several planar graph algorithms. We investigate the extent to which similar relations hold in other graph families. We show that treewidth is bounded by a function of the diameter in a
Approximate MRF Inference Using Bounded Treewidth Subgraphs
"... Graph cut algorithms [9], commonly used in computer vision, solve a firstorder MRF over binary variables. The state of the art for this NPhard problem is QPBO [1, 2], which finds the values for a subset of the variables in the global minimum. While QPBO is very effective overall there are still ..."
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Cited by 3 (0 self)
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, but which for which exact inference can be done efficiently. Our Bounded Treewidth Subgraph (kBTS) algorithm greedily computes a large weight treewidthk subgraph of the signed graph, then solves the energy minimization problem for this subgraph by dynamic programming. The edges omitted by our greedy
Strong backdoors to bounded treewidth SAT
 In 54th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2013
, 2013
"... There are various approaches to exploiting “hidden structure ” in instances of hard combinatorial problems to allow faster algorithms than for general unstructured or random instances. For SAT and its counting version #SAT, hidden structure has been exploited in terms of decomposability and strong b ..."
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Cited by 3 (2 self)
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backdoor sets. Decomposability can be considered in terms of the treewidth of a graph that is associated with the given CNF formula, for instance by considering clauses and variables as vertices of the graph, and making a variable adjacent with all the clauses it appears in. On the other hand, a strong
Efficient frequent connected subgraph mining in graphs of bounded treewidth
 In Proc. ECML/PKDD
, 2008
"... Abstract. The frequent connected subgraph mining problem, i.e., the problem of listing all connected graphs that are subgraph isomorphic to at least a certain number of transaction graphs of a database, cannot be solved in output polynomial time in the general case. If, however, the transaction grap ..."
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Cited by 4 (0 self)
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graphs are restricted to forests then the problem becomes tractable. In this paper we generalize the positive result on forests to graphs of bounded treewidth. In particular, we show that for this class of transaction graphs, frequent connected subgraphs can be listed in incremental polynomial time
Results 1  10
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5,581