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On treewidth approximations [PDF]
Discrete Applied Mathematics, 2004 We introduce a natural heuristic for approximating the treewidth of graphs. We prove that this heuristic gives a constant factor approximation for the treewidth of graphs with bounded asteroidal number.
D Kratsch
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Discrete Mathematics, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arie M.C.A. Koster, Hans L. Bodlaender
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Journal of Algorithms, 1997
Summary: We consider a special variant of tree-decompositions, called domino tree-decompositions, and the related notion of domino treewidth. In a domino tree- decomposition, each vertex of the graph belongs to at most two nodes of the tree. We prove that for every \(k\), \(d\), there exists a constant \(c_{k,d}\) such that a graph with treewidth at ...
Bodlaender, Hans, Engelfriet, Joost
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Summary: We consider a special variant of tree-decompositions, called domino tree-decompositions, and the related notion of domino treewidth. In a domino tree- decomposition, each vertex of the graph belongs to at most two nodes of the tree. We prove that for every \(k\), \(d\), there exists a constant \(c_{k,d}\) such that a graph with treewidth at ...
Bodlaender, Hans, Engelfriet, Joost
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Treewidth computations II. Lower bounds [PDF]
Information and Computation, 2011 For several applications, it is important to be able to compute the treewidth of a given graph and to find tree decompositions of small width reasonably fast.
Arie M.C.A. Koster, Hans L. Bodlaender
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Journal of Combinatorial Theory Series B, 2018 The treewidth of a graph is an important invariant in structural and algorithmic graph theory. This paper studies the treewidth of line graphs. We show that determining the treewidth of the line graph of a graph $G$ is equivalent to determining the minimum vertex congestion of an embedding of $G$ into a tree.
David Wood, Daniel John Harvey
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A Note on Multiflows and Treewidth
Algorithmica, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chandra Chekuri +2 more
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Approximation Algorithms for Treewidth
Algorithmica, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2014
• O.k p log k/. • For all {v;w} 2 E, there is an i 2 I with v, w 2 Xi . • For all v 2 V , the set {i 2 I jv 2 Xi} induces a connected subtree of T . The width of a tree decomposition is max i2I jXi j 1, and the treewidth of a graph G is the minimum width of a tree decomposition of G (Fig. 1). An alternative definition is in terms of chordal graphs.
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• O.k p log k/. • For all {v;w} 2 E, there is an i 2 I with v, w 2 Xi . • For all v 2 V , the set {i 2 I jv 2 Xi} induces a connected subtree of T . The width of a tree decomposition is max i2I jXi j 1, and the treewidth of a graph G is the minimum width of a tree decomposition of G (Fig. 1). An alternative definition is in terms of chordal graphs.
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2009
One of the most important structural parameters of graphs is treewidth , a measure for the "tree-likeness" and thus in many cases an indicator for the hardness of problem instances. The smaller the treewidth, the closer the graph is to a tree and the more efficiently the underlying instance often can be solved.
Marko Samer, Helmut Veith
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One of the most important structural parameters of graphs is treewidth , a measure for the "tree-likeness" and thus in many cases an indicator for the hardness of problem instances. The smaller the treewidth, the closer the graph is to a tree and the more efficiently the underlying instance often can be solved.
Marko Samer, Helmut Veith
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On the Treewidth of NK Landscapes
2003The concepts of treewidth and tree-decomposition on graphs generalize those of the trees. It is well established that when restricted to instances with a bounded treewidth, many NP hard problems can be solved polynomially. In this paper, we study the treewidth of the NK landscape models.
Yong Gao 0001, Joseph C. Culberson
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