Displaying similar documents to “Exploiting Tree Decomposition for Guiding Neighborhoods Exploration for VNS”

A note on domino treewidth.

Bodlaender, Hans L. (1999)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

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Spanning tree congestion of rook's graphs

Kyohei Kozawa, Yota Otachi (2011)

Discussiones Mathematicae Graph Theory

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Let G be a connected graph and T be a spanning tree of G. For e ∈ E(T), the congestion of e is the number of edges in G joining the two components of T - e. The congestion of T is the maximum congestion over all edges in T. The spanning tree congestion of G is the minimum congestion over all its spanning trees. In this paper, we determine the spanning tree congestion of the rook's graph Kₘ ☐ Kₙ for any m and n.

Completely Independent Spanning Trees in (Partial) k-Trees

Masayoshi Matsushita, Yota Otachi, Toru Araki (2015)

Discussiones Mathematicae Graph Theory

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Two spanning trees T1 and T2 of a graph G are completely independent if, for any two vertices u and v, the paths from u to v in T1 and T2 are internally disjoint. For a graph G, we denote the maximum number of pairwise completely independent spanning trees by cist(G). In this paper, we consider cist(G) when G is a partial k-tree. First we show that [k/2] ≤ cist(G) ≤ k − 1 for any k-tree G. Then we show that for any p ∈ {[k/2], . . . , k − 1}, there exist infinitely many k-trees G such...

A characterization of (γₜ,γ₂)-trees

You Lu, Xinmin Hou, Jun-Ming Xu, Ning Li (2010)

Discussiones Mathematicae Graph Theory

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Let γₜ(G) and γ₂(G) be the total domination number and the 2-domination number of a graph G, respectively. It has been shown that: γₜ(T) ≤ γ₂(T) for any tree T. In this paper, we provide a constructive characterization of those trees with equal total domination number and 2-domination number.

A lower bound for the irredundance number of trees

Michael Poschen, Lutz Volkmann (2006)

Discussiones Mathematicae Graph Theory

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Let ir(G) and γ(G) be the irredundance number and domination number of a graph G, respectively. The number of vertices and leaves of a graph G are denoted by n(G) and n₁(G). If T is a tree, then Lemańska [4] presented in 2004 the sharp lower bound γ(T) ≥ (n(T) + 2 - n₁(T))/3. In this paper we prove ir(T) ≥ (n(T) + 2 - n₁(T))/3. for an arbitrary tree T. Since γ(T) ≥ ir(T) is always valid, this inequality is an extension and improvement of...