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Treewidth Is NP-Complete on Cubic Graphs
International Symposium on Parameterized and Exact ComputationIn this paper, we show that Treewidth is NP-complete for cubic graphs, thereby improving the result by Bodlaender and Thilikos from 1997 that Treewidth is NP-complete on graphs with maximum degree at most 9.
H. Bodlaender +8 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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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\}
C. Pandu Rangan +2 more
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Treewidth: Structure and Algorithms
2007This paper surveys some aspects of the graph theoretic notion of treewidth. In particular, we look at the interaction between different characterizations of the notion, and algorithms and algorithmic applications.
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Orthogonal planarity testing of bounded treewidth graphs
Journal of computer and system sciences (Print), 2021E. D. Giacomo +2 more
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, 2013