A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2004; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
New Graph Classes of Bounded Clique-Width

2004
*
Theory of Computing Systems
*

LinEMSOL(τ1,L) by Courcelle, Makowsky

doi:10.1007/s00224-004-1154-6
fatcat:a3yucbewjvgejikclpwtxnym3y
*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 ...##
###
New Graph Classes of Bounded Clique-Width
[chapter]

2002
*
Lecture Notes in Computer Science
*

LinEMSOL(τ1,L) by Courcelle, Makowsky

doi:10.1007/3-540-36379-3_6
fatcat:retqdsicjfcxbhxunm2334ycoi
*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 ...##
###
Stability number of bull- and chair-free graphs revisited

2003
*
Discrete Applied Mathematics
*

This implies constant-bounded

doi:10.1016/s0166-218x(02)00415-8
fatcat:vjokgbfafzbltiuxl66ercn5zu
*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. ...##
###
(P5,diamond)-free graphs revisited: structure and linear time optimization

2004
*
Discrete Applied Mathematics
*

Using the concept

doi:10.1016/s0166-218x(03)00266-x
fatcat:54ihrkjzlnc3holpwtjzzcyy54
*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. ...##
###
Infinitely many minimal classes of graphs of unbounded clique-width
[article]

2017
*
arXiv
*
pre-print

The celebrated theorem

arXiv:1701.08857v1
fatcat:rq5rj3mn7bg35jmzor6nt4urly
*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. ...##
###
Clique-Width for Hereditary Graph Classes
[article]

2019
*
arXiv
*
pre-print

We also explain a possible strong connection

arXiv:1901.00335v2
fatcat:3mb44qloc5cxxddyimwo6horqa
*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. ...##
###
On variations of P4-sparse graphs

2003
*
Discrete Applied Mathematics
*

These

doi:10.1016/s0166-218x(03)00180-x
fatcat:i2uxfgl4tzbijp74otjkid5qmm
*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 ...##
###
Infinitely many minimal classes of graphs of unbounded clique-width

2018
*
Discrete Applied Mathematics
*

The celebrated theorem

doi:10.1016/j.dam.2017.02.012
fatcat:vmtfbgjfbbgxfiwse63mnzp5f4
*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. ...##
###
Recent developments on graphs of bounded clique-width

2009
*
Discrete Applied Mathematics
*

solutions when restricted to

doi:10.1016/j.dam.2008.08.022
fatcat:h45w5c3pfrazbgyfboniyohhha
*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*...##
###
Linear layouts measuring neighbourhoods in graphs

2006
*
Discrete Mathematics
*

We show that the neighbourhood-

doi:10.1016/j.disc.2006.03.048
fatcat:msxln5bidvbx7ocos7yiv7xnza
*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] ). ...##
###
Thread Graphs, Linear Rank-Width and Their Algorithmic Applications
[chapter]

2011
*
Lecture Notes in Computer Science
*

We first provide a characterization

doi:10.1007/978-3-642-19222-7_5
fatcat:luuytuxq2jao7eva5cpygbihqi
*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. ...##
###
P6- and triangle-free graphs revisited: structure and bounded clique-width

2006
*
Discrete Mathematics & Theoretical Computer Science
*

P6-free

doi:10.46298/dmtcs.372
fatcat:kapajguzczfh3lxsf3poeih7ty
*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 ...##
###
Classifying the clique-width of H-free bipartite graphs

2016
*
Discrete Applied Mathematics
*

2016) 'Classifying the

doi:10.1016/j.dam.2015.06.030
fatcat:yec44zug5bayjexahk42utabai
*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*. ...##
###
Classifying the Clique-Width of H-Free Bipartite Graphs
[chapter]

2014
*
Lecture Notes in Computer Science
*

2016) 'Classifying the

doi:10.1007/978-3-319-08783-2_42
fatcat:rmosfozfobd6bm2fhygsu44e3i
*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*. ...##
###
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*...
« Previous

*Showing results 1 — 15 out of 2,926 results*