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New Graph Classes of Bounded Clique-Width

Andreas Brandstädt, Feodor F. Dragan, Hoàng-Oanh Le, Raffaele Mosca
2004 Theory of Computing Systems  
LinEMSOL(τ1,L) by Courcelle, Makowsky and Rotics, is solvable in linear time on any graph class with bounded clique-width for which a k-expression for the input graph can be constructed in linear time  ...  The concept of clique-width extends the one of treewidth since bounded treewidth implies bounded clique-width.  ...  It is straightforward to see that the clique-width of matched co-bipartite (comatched bipartite) graphs, bipartite chain (co-bipartite chain) graphs as well as the clique-width of induced paths and cycles  ... 
doi:10.1007/s00224-004-1154-6 fatcat:a3yucbewjvgejikclpwtxnym3y

New Graph Classes of Bounded Clique-Width [chapter]

Andreas Brandstädt, Feodor F. Dragan, Hoàng-Oanh Le, Raffaele Mosca
2002 Lecture Notes in Computer Science  
LinEMSOL(τ1,L) by Courcelle, Makowsky and Rotics, is solvable in linear time on any graph class with bounded clique-width for which a k-expression for the input graph can be constructed in linear time  ...  The concept of clique-width extends the one of treewidth since bounded treewidth implies bounded clique-width.  ...  It is straightforward to see that the clique-width of matched co-bipartite (comatched bipartite) graphs, bipartite chain (co-bipartite chain) graphs as well as the clique-width of induced paths and cycles  ... 
doi:10.1007/3-540-36379-3_6 fatcat:retqdsicjfcxbhxunm2334ycoi

Stability number of bull- and chair-free graphs revisited

Andreas Brandstädt, Chı́nh T Hoàng, Van Bang Le
2003 Discrete Applied Mathematics  
This implies constant-bounded clique width for these graph classes which leads to linear time algorithms for some algorithmic problems.  ...  De Simone showed that prime bull-and chair-free graphs containing a co-diamond are either bipartite or an induced cycle of odd length at least ÿve.  ...  The clique width of a graph is the maximum of the clique width of its prime graphs, and the clique width of the complement graph G of a graph G is at most twice the clique width of G.  ... 
doi:10.1016/s0166-218x(02)00415-8 fatcat:vjokgbfafzbltiuxl66ercn5zu

(P5,diamond)-free graphs revisited: structure and linear time optimization

Andreas Brandstädt
2004 Discrete Applied Mathematics  
Using the concept of prime graphs and modular decomposition of graphs, we give a complete structure description of (P5,diamond)-free graphs implying that these graphs have bounded clique width (the P5  ...  The structure and bounded clique width of this graph class allows to solve several algorithmic problems on this class in linear time, among them the problems Maximum Weight Stable Set (MWS), Maximum Weight  ...  The clique width of a graph is the maximum of the clique width of its prime subgraphs, and the clique width of the complement graph G of G is at most twice the clique width of G.  ... 
doi:10.1016/s0166-218x(03)00266-x fatcat:54ihrkjzlnc3holpwtjzzcyy54

Infinitely many minimal classes of graphs of unbounded clique-width [article]

A. Collins, J. Foniok, N. Korpelainen, V. Lozin, V. Zamaraev
2017 arXiv   pre-print
The celebrated theorem of Robertson and Seymour states that in the family of minor-closed graph classes, there is a unique minimal class of graphs of unbounded tree-width, namely, the class of planar graphs  ...  This, however, is not the case with respect to clique-width, as the clique-width of a graph can be (much) smaller than the clique-width of its minor.  ...  Clearly, lcwd(G) ≥ cwd(G) and there are classes of graphs for which the difference between clique-width and linear clique-width can be arbitrarily large (see e.g.  ... 
arXiv:1701.08857v1 fatcat:rq5rj3mn7bg35jmzor6nt4urly

Clique-Width for Hereditary Graph Classes [article]

Konrad K. Dabrowski, Matthew Johnson, Daniël Paulusma
2019 arXiv   pre-print
We also explain a possible strong connection between results on boundedness of clique-width and on well-quasi-orderability by the induced subgraph relation for hereditary graph classes.  ...  For this reason, the boundedness or unboundedness of clique-width has been investigated and determined for many graph classes.  ...  In contrast, we recall that it is not yet clear if the classifications for boundedness of cliquewidth on H-free bipartite graphs and (K 3 , H)-free graphs also coincide; see Open Problem 4.20.  ... 
arXiv:1901.00335v2 fatcat:3mb44qloc5cxxddyimwo6horqa

On variations of P4-sparse graphs

Andreas Brandstädt, Raffaele Mosca
2003 Discrete Applied Mathematics  
These graphs attracted considerable attention in connection with the P4-structure of graphs and the fact that P4-sparse graphs have bounded clique-width.  ...  We give a complete classiÿcation with respect to clique-width of all superclasses of P4-sparse graphs deÿned by forbidden P4 extensions by one vertex which are not P4-sparse, i.e. the P5, chair, P, C5  ...  Acknowledgements We are grateful to two anonymous referees for some comments which helped to improve the presentation of this note and in particular to simplify the proof of Lemma 3, as proposed by one  ... 
doi:10.1016/s0166-218x(03)00180-x fatcat:i2uxfgl4tzbijp74otjkid5qmm

Infinitely many minimal classes of graphs of unbounded clique-width

A. Collins, J. Foniok, N. Korpelainen, V. Lozin, V. Zamaraev
2018 Discrete Applied Mathematics  
The celebrated theorem of Robertson and Seymour states that in the family of minor-closed graph classes, there is a unique minimal class of graphs of unbounded tree-width, namely, the class of planar graphs  ...  This, however, is not the case with respect to clique-width, as the clique-width of a graph can be (much) smaller than the clique-width of its minor.  ...  Clearly, lcwd(G) ≥ cwd(G) and there are classes of graphs for which the difference between clique-width and linear clique-width can be arbitrarily large (see e.g.  ... 
doi:10.1016/j.dam.2017.02.012 fatcat:vmtfbgjfbbgxfiwse63mnzp5f4

Recent developments on graphs of bounded clique-width

Marcin Kamiński, Vadim V. Lozin, Martin Milanič
2009 Discrete Applied Mathematics  
solutions when restricted to graphs of bounded clique-width.  ...  Whether the clique-width of graphs in a certain class of graphs is bounded or not, is an important question from an algorithmic point of view, as many problems that are NPhard in general admit polynomial-time  ...  As an immediate consequence of Theorem 1, we conclude that the clique-width of bipartite, co-bipartite and split graphs is unbounded (a direct proof of unboundedness of the clique-width of split graphs  ... 
doi:10.1016/j.dam.2008.08.022 fatcat:h45w5c3pfrazbgyfboniyohhha

Linear layouts measuring neighbourhoods in graphs

Frank Gurski
2006 Discrete Mathematics  
We show that the neighbourhood-width of a graph differs from its linear clique-width or linear NLC-width at most by one.  ...  Furthermore, we prove that simple modifications of neighbourhood-width imply equivalent layout characterizations for linear clique-width and linear NLC-width.  ...  The graph defined by expression X is denoted by val(X). There is a very close relation between the linear NLC-width and linear clique-width of a graph. [20] ).  ... 
doi:10.1016/j.disc.2006.03.048 fatcat:msxln5bidvbx7ocos7yiv7xnza

Thread Graphs, Linear Rank-Width and Their Algorithmic Applications [chapter]

Robert Ganian
2011 Lecture Notes in Computer Science  
We first provide a characterization of graphs of linear rank-width 1 and then show that on such graphs it is possible to obtain better algorithmic results than on distance hereditary graphs and even trees  ...  Specifically, we provide polynomial algorithms for computing path-width, dominating bandwidth and a 2-approximation of ordinary bandwidth on graphs of linear rank-width 1.  ...  Acknowledgment The author wishes to thank Jan Obdržálek for his contribution and help in characterizing graphs of linear rank-width 1.  ... 
doi:10.1007/978-3-642-19222-7_5 fatcat:luuytuxq2jao7eva5cpygbihqi

P6- and triangle-free graphs revisited: structure and bounded clique-width

Andreas Brandstädt, Tilo Klembt, Suhail Mahfud
2006 Discrete Mathematics & Theoretical Computer Science  
P6-free graphs have bounded clique-width.  ...  It turns out that the structure of these graphs is extremely simple implying bounded clique-width and thus, efficient algorithms exist for all problems expressible in terms of Monadic Second Order Logic  ...  Acknowledgements We are grateful to Van Bang Le for helpful discussions and to three anonymous referees for their valuable comments which lead to considerable improvements in the presentation of our results  ... 
doi:10.46298/dmtcs.372 fatcat:kapajguzczfh3lxsf3poeih7ty

Classifying the clique-width of H-free bipartite graphs

Konrad K. Dabrowski, Daniël Paulusma
2016 Discrete Applied Mathematics  
2016) 'Classifying the clique-width of H-free bipartite graphs.', Discrete applied mathematics., 200 . pp. 43-51.  ...  We say that a class of graphs has bounded clique-width if every graph from the class has clique-width at most c for some constant c.  ...  weakly chordal graphs of bounded and unbounded clique-width.  ... 
doi:10.1016/j.dam.2015.06.030 fatcat:yec44zug5bayjexahk42utabai

Classifying the Clique-Width of H-Free Bipartite Graphs [chapter]

Konrad Kazimierz Dabrowski, Daniël Paulusma
2014 Lecture Notes in Computer Science  
2016) 'Classifying the clique-width of H-free bipartite graphs.', Discrete applied mathematics., 200 . pp. 43-51.  ...  We say that a class of graphs has bounded clique-width if every graph from the class has clique-width at most c for some constant c.  ...  weakly chordal graphs of bounded and unbounded clique-width.  ... 
doi:10.1007/978-3-319-08783-2_42 fatcat:rmosfozfobd6bm2fhygsu44e3i

Page 9589 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews  
Summary: “A bipartite graph is chordal bipartite if every cycle of length at least six has a chord. In the class of chordal bipartite graphs the tree-width and the clique-width are unbounded.  ...  “Our main results are that chordal bipartite graphs of bounded vertex degree have bounded tree-width and that k-fork-free chordal bipartite graphs have bounded clique-width, where a k-fork is the graph  ... 
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