The Tree-Width of Clique-Width Bounded Graphs without Kn,n

Gurski, Frank; Wanke, Egon

doi:10.1007/3-540-40064-8_19

Cited by 71 publications

(61 citation statements)

References 10 publications

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“…Fact 18 [11] Let C be a class of graphs whose degree is bounded by n and whose clique-width is bounded by k. Then, C has tree-width bounded by 3k(n − 1) − 1.…”

Section: Clique Widthmentioning

confidence: 99%

MSO Decidability of Multi-Pushdown Systems via Split-Width

Aiswarya

Gastin

Kumar

2012

Lecture Notes in Computer Science

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Abstract. Multi-threaded programs with recursion are naturally modeled as multi-pushdown systems. The behaviors are represented as multiply nested words (MNWs), which are words enriched with additional binary relations for each stack matching a push operation with the corresponding pop operation. Any MNW can be decomposed by two basic and natural operations: shuffle of two sequences of factors and merge of consecutive factors of a sequence. We say that the split-width of an MNW is k if it admits a decomposition where the number of factors in each sequence is at most k. The MSO theory of MNWs with split-width k is decidable. We introduce two very general classes of MNWs that strictly generalize known decidable classes and prove their MSO decidability via their split-width and obtain comparable or better bounds of tree-width of known classes.

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“…Fact 18 [11] Let C be a class of graphs whose degree is bounded by n and whose clique-width is bounded by k. Then, C has tree-width bounded by 3k(n − 1) − 1.…”

Section: Clique Widthmentioning

confidence: 99%

MSO Decidability of Multi-Pushdown Systems via Split-Width

Aiswarya

Gastin

Kumar

2012

Lecture Notes in Computer Science

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“…In what is perhaps the most surprising result of this paper, we show that Edge Hamiltonian Cycle remains FPT even for clique-width, despite this parameter's additional generality. On a high level, our strategy is to rely on a characterization of bounded clique-width graphs given by Gurski and Wanke [19] which states roughly that if a graph has small clique-width and no large complete bipartite subgraphs, then it has small treewidth. We devise an algorithm that locates and "reduces" large complete bipartite subgraphs in the input graph, without affecting the answer or increasing the clique-width.…”

Section: Overview Of Resultsmentioning

confidence: 99%

“…By repeatedly applying this step we end up with a graph of small treewidth for which the problem is FPT. We believe this idea, which is a rare algorithmic application of the characterization of [19], may be of independent interest.…”

Section: Overview Of Resultsmentioning

confidence: 99%

Parameterized Edge Hamiltonicity

Lampis

Makino

Mitsou

et al. 2014

Graph-Theoretic Concepts in Computer Science

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Abstract. We study the parameterized complexity of the classical Edge Hamiltonian Path problem and give several fixed-parameter tractability results. First, we settle an open question of Demaine et al. by showing that Edge Hamiltonian Path is FPT parameterized by vertex cover, and that it also admits a cubic kernel. We then show fixed-parameter tractability even for a generalization of the problem to arbitrary hypergraphs, parameterized by the size of a (supplied) hitting set. We also consider the problem parameterized by treewidth or clique-width. Surprisingly, we show that the problem is FPT for both of these standard parameters, in contrast to its vertex version, which is W-hard for cliquewidth. Our technique, which may be of independent interest, relies on a structural characterization of clique-width in terms of treewidth and complete bipartite subgraphs due to Gurski and Wanke.

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“…For proving (2), the authors construct graphs of tree-width 2k and clique-width larger than 2 k−1 . Assertion (3) is proved in [31] (also [18], Proposition 2.115).…”

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confidence: 82%

On quasi-planar graphs: Clique-width and logical description

Courcelle

2020

Discrete Applied Mathematics

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Motivated by the construction of FPT graph algorithms parameterized by clique-width or tree-width, we study graph classes for which treewidth and clique-width are linearly related. This is the case for all graph classes of bounded expansion, but in view of concrete applications, we want to have "small" constants in the comparisons between these width parameters.We focus our attention on graphs that can be drawn in the plane with limited edge crossings, for an example, at most p crossings for each edge. These graphs are called p-planar. We consider a more general situation where the graph of edge crossings must belong to a fixed class of graphs D. For p-planar graphs, D is the class of graphs of degree at most p. We prove that tree-width and clique-width are linearly related for graphs drawable with a graph of crossings of bounded average degree.We prove that the class of 1-planar graphs, although conceptually close to that of planar graphs, is not characterized by a monadic second-order sentence. We identify two subclasses that are.

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The Tree-Width of Clique-Width Bounded Graphs without Kn,n

Cited by 71 publications

References 10 publications

MSO Decidability of Multi-Pushdown Systems via Split-Width

MSO Decidability of Multi-Pushdown Systems via Split-Width

Parameterized Edge Hamiltonicity

On quasi-planar graphs: Clique-width and logical description

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