Recent developments on graphs of bounded clique-width

Kamiński, Marcin; Lozin, Vadim V.; Milanič, Martin

doi:10.1016/j.dam.2008.08.022

Cited by 105 publications

(115 citation statements)

References 44 publications

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“…The next well-known lemma follows from combining Fact 3 with the fact that walls have maximum degree 3 and unbounded clique-width (see e.g. [21]). …”

Section: Facts About Clique-widthmentioning

confidence: 99%

“…For a class of graphs G of bounded maximum degree, let G be a class of graphs that is (∞, es)-obtained from G, where es is the edge subdivision operation. Then G has bounded clique-width if and only if G has bounded clique-width [21].…”

Section: Facts About Clique-widthmentioning

confidence: 99%

“…We say that a bipartite graph G is strongly H-free if no bipartition of G contains an induced copy of H in a way that respects the bipartition of H. Strongly H-free graphs have been studied with respect to their clique-width, although under less explicit terminology (see e.g. [21,24,25]). In particular, Lozin and Volz [25] completely determined those bipartite graphs H, for which the class of strongly H-free graphs has bounded clique-width (we give an exact statement of their result in Section 3).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Classifying the clique-width of H-free bipartite graphs

Dabrowski

Paulusma

2016

Discrete Applied Mathematics

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract. Let G be a bipartite graph, and let H be a bipartite graph with a fixed bipartition (BH , WH ). We consider three different, natural ways of forbidding H as an induced subgraph in G.

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“…The next well-known lemma follows from combining Fact 3 with the fact that walls have maximum degree 3 and unbounded clique-width (see e.g. [21]). …”

Section: Facts About Clique-widthmentioning

confidence: 99%

Section: Facts About Clique-widthmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Classifying the clique-width of H-free bipartite graphs

Dabrowski

Paulusma

2016

Discrete Applied Mathematics

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“…On the other hand, our lower bound technique based on expander graphs essentially requires bounded degree, but the candidate classes for improving lower bounds in our hierarchy, bounded clique-width CNFs and beta acyclic CNFs, have unbounded degree. In both cases, imposing a degree bound leads to classes of bounded treewidth [18] and thus polynomial bounds on the size of OBDD representations.…”

Section: Resultsmentioning

confidence: 99%

On Compiling Structured CNFs to OBDDs

Bova

Slivovsky

2016

Theory Comput Syst

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We present new results on the size of OBDD representations of structurally characterized classes of CNF formulas. First, we prove that variable convex formulas (that is, formulas with incidence graphs that are convex with respect to the set of variables) have polynomial OBDD size. Second, we prove an exponential lower bound on the OBDD size of a family of CNF formulas with incidence graphs of bounded degree. We obtain the first result by identifying a simple sufficient condition-which we call the few subterms property-for a class of CNF formulas to have polynomial OBDD size, and show that variable convex formulas satisfy this condition. To prove the second result, we exploit the combinatorial properties of expander graphs; this approach allows us to establish an exponential lower bound on the OBDD size of formulas satisfying strong syntactic restrictions.

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“…(3) Graph classes of bounded clique-width are studied in several articles [9,10,33]. It would be interesting to have classes of unbounded clique-with for which cwd(G) = O(twd(G) α ) where 0 < α < 1.…”

mentioning

confidence: 99%

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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Recent developments on graphs of bounded clique-width

Cited by 105 publications

References 44 publications

Classifying the clique-width of H-free bipartite graphs

Classifying the clique-width of H-free bipartite graphs

On Compiling Structured CNFs to OBDDs

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

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