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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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A Note on Multiflows and Treewidth
Algorithmica, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chekuri, Chandra +2 more
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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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Approximation Algorithms for Treewidth
Algorithmica, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Treewidth of Circular-Arc Graphs
SIAM Journal on Discrete Mathematics, 1994It is shown that the treewidth of circular-arc graphs and the corresponding tree-decomposition can be found in \(O(n^ 3)\) time. Let \(G= (V,E)\) be a circular-arc graph corresponding to a family \(\{A_ 0, A_ 1,\dots, A_{n-1}\}\) of arcs on a unit circle. Define a left clique \(S_ i\) by \(S_ i= \{A_ j\mid A_ j\) contains the left end points of \(A_ i\}
Sundaram, Ravi +2 more
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