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On the Clique—Width of Perfect Graph Classes [chapter]

Martin Charles Golumbic, Udi Rotics
1999 Lecture Notes in Computer Science  
In this paper we study the clique-width of perfect graph classes.  ...  On the other hand, we show that the classes of unit interval and permutation graphs are not of bounded clique-width.  ...  In this paper we study the clique-width of perfect graph classes. We first show that: Theorem 1.  ... 
doi:10.1007/3-540-46784-x_14 fatcat:xaswhk2jlbhsph4vyakmka5nne

ON THE CLIQUE-WIDTH OF SOME PERFECT GRAPH CLASSES

MARTIN CHARLES GOLUMBIC, UDI ROTICS
2000 International Journal of Foundations of Computer Science  
In this paper we study the clique{width of perfect graph classes.  ...  On the other hand, we show that the classes of unit interval and permutation graphs are not of bounded clique{width.  ...  Acknowledgments We are grateful to an anonymous referee for his valuable comments and suggestions which helped to improve the content of this paper.  ... 
doi:10.1142/s0129054100000260 fatcat:ltltzvwj2zd2vgygipnhz2koey

Bounding clique-width via perfect graphs

Konrad K. Dabrowski, Shenwei Huang, Daniël Paulusma
2016 Journal of computer and system sciences (Print)  
We continue a recent study into the clique-width of (H1, H2)-free graphs and present three new classes of (H1, H2)-free graphs that have bounded clique-width.  ...  To prove boundedness of their clique-width we develop a technique based on bounding clique covering number in combination with reduction to subclasses of perfect graphs.  ...  The second author is grateful for the generous support of the Graduate (International) Research Travel Award from Simon Fraser University and Dr. Pavol Hell's NSERC Discovery Grant.  ... 
doi:10.1016/j.jcss.2016.06.007 fatcat:7g5jkpjzrjdpzpvphckhyzly2m

Bounding the Clique-Width of H -free Split Graphs

Andreas Brandstädt, Konrad K. Dabrowski, Shenwei Huang, Daniël Paulusma
2015 Electronic Notes in Discrete Mathematics  
We continue a study into the boundedness of clique-width of subclasses of perfect graphs. We identify five new classes of H-free split graphs whose clique-width is bounded.  ...  of H-free split graphs has bounded clique-width.  ...  In this paper we continue a study into the boundedness of the clique-width of subclasses of perfect graphs. Clique-width is still one of the most difficult graph parameters to deal with.  ... 
doi:10.1016/j.endm.2015.06.069 fatcat:lmd35ycrcvdxxco3mnbkzmgz74

Characterizations for co-graphs defined by restricted NLC-width or clique-width operations

Frank Gurski
2006 Discrete Mathematics  
Since (C 4 , P 4 )-free graphs are exactly trivially perfect graphs, the set of graphs of NLCT-width 1 is equal to the set of trivially perfect graphs, and a recursive definition for trivially perfect  ...  Further we show that a graph has linear NLC-width 1 if and only if is (C 4 , P 4 , 2K 2 )-free. This implies that the set of graphs of linear NLC-width 1 is equal to the set of threshold graphs.  ...  on graph classes of bounded linear NLC-width or bounded NLCT-width and corresponding restrictions for the operations of clique-width can be found in [12] .  ... 
doi:10.1016/j.disc.2005.11.014 fatcat:rmg5bcys7bekjdsdd7tatpmysi

Bounding Clique-Width via Perfect Graphs [article]

Konrad K. Dabrowski and Shenwei Huang and Daniël Paulusma
2015 arXiv   pre-print
We continue a recent study into the clique-width of (H_1,H_2)-free graphs and present three new classes of (H_1,H_2)-free graphs of bounded clique-width and one of unbounded clique-width.  ...  To prove boundedness of clique-width for the first three cases we develop a technique based on bounding clique covering number in combination with reduction to subclasses of perfect graphs.  ...  Nevertheless, many NP-complete graph problems are solvable in polynomial time on graph classes of bounded clique-width, that is, classes in which the clique-width of each of its graphs is at most c for  ... 
arXiv:1406.6298v2 fatcat:hi3xhcfnqzew3kvqhpsxcwsz5i

Acyclic coloring of special digraphs [article]

Frank Gurski and Dominique Komander and Carolin Rehs
2020 arXiv   pre-print
For directed co-graphs, which is a class of digraphs of directed clique-width 2, and several generalizations we even show linear time solutions for computing the dichromatic number.  ...  We introduce the first polynomial-time algorithm for the acyclic coloring problem on digraphs of constant directed clique-width.  ...  Acknowledgements The work of the second and third author was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) -388221852  ... 
arXiv:2006.13911v3 fatcat:metx5oprwzefjnjf445a7ord2y

Bounding Clique-Width via Perfect Graphs [chapter]

Konrad Kazimierz Dabrowski, Shenwei Huang, Daniël Paulusma
2015 Lecture Notes in Computer Science  
We continue a recent study into the clique-width of (H1, H2)-free graphs and present three new classes of (H1, H2)-free graphs that have bounded clique-width.  ...  The three new graph classes have in common that one of their two forbidden induced subgraphs is the diamond (the graph obtained from a clique on four vertices by deleting one edge).  ...  We show that besides the class of bipartite graphs, the class of chordal graphs and the class of perfect graphs itself may be used for Step 1.  ... 
doi:10.1007/978-3-319-15579-1_53 fatcat:pz4tanvg5vd6hnuibmsbf5mlhu

Bounding the clique-width of H-free split graphs

Andreas Brandstädt, Konrad K. Dabrowski, Shenwei Huang, Daniël Paulusma
2016 Discrete Applied Mathematics  
We continue a study into the boundedness of clique-width of subclasses of perfect graphs. We identify five new classes of H-free split graphs whose clique-width is bounded.  ...  of H-free split graphs has bounded clique-width.  ...  A graph class is said to be of bounded clique-width if there is a constant c such that the clique-width of every graph in the class is at most c.  ... 
doi:10.1016/j.dam.2016.04.003 fatcat:nhfo7zwuona2dg4cxld5mum4i4

Bounding the Clique-Width of H-free Split Graphs [article]

Andreas Brandstädt, Konrad K. Dabrowski, Shenwei Huang, Daniël Paulusma
2015 arXiv   pre-print
A graph is H-free if it has no induced subgraph isomorphic to H. We continue a study into the boundedness of clique-width of subclasses of perfect graphs.  ...  We identify five new classes of H-free split graphs whose clique-width is bounded.  ...  A graph class is said to be of bounded clique-width if there is a constant c such that the clique-width of every graph in the class is at most c.  ... 
arXiv:1509.04273v1 fatcat:jbv3ad4dhnf2tjohtnd5yyg55q

Page 4430 of Mathematical Reviews Vol. , Issue 2001G [page]

2001 Mathematical Reviews  
ON) On the clique-width of some perfect graph classes.  ...  “In this paper we study the clique-width of perfect graph classes.  ... 

A comparison of two approaches for polynomial time algorithms computing basic graph parameters [article]

Frank Gurski
2008 arXiv   pre-print
We also present linear time algorithms for computing the latter four basic graph parameters on trees, i.e. graphs of tree-width 1, and on co-graphs, i.e. graphs of clique-width at most 2.  ...  In this paper we compare and illustrate the algorithmic use of graphs of bounded tree-width and graphs of bounded clique-width.  ...  On the one hand, clique-width allows to define larger classes of graphs of bounded width than tree-width.  ... 
arXiv:0806.4073v1 fatcat:ho5spatm6fb4pculjjptzegwhi

On rank-width of even-hole-free graphs [article]

Isolde Adler, Ngoc Khang Le, Haiko Müller, Marko Radovanović, Nicolas Trotignon, Kristina Vušković
2017 arXiv   pre-print
We present a class of (diamond, even hole)-free graphs with no clique cutset that has unbounded rank-width.  ...  A natural question is to ask, whether even-hole-free graphs with no clique cutsets have bounded rank-width. Our result gives a negative answer.  ...  In contrast, there exist dense graph classes with bounded clique-width. This makes clique-width particularly interesting in the study of algorithmic properties of hereditary graph classes.  ... 
arXiv:1611.09907v2 fatcat:hgtsktipz5gytac7dkcjlz62le

Bounding the Clique-Width of H-free Chordal Graphs [chapter]

Andreas Brandstädt, Konrad K. Dabrowski, Shenwei Huang, Daniël Paulusma
2015 Lecture Notes in Computer Science  
We illustrate the usefulness of this classification for classifying other types of graph classes by proving that the class of (2P1 + P3, K4)-free graphs has bounded clique-width via a reduction to K4-free  ...  In particular, we prove that the clique-width is: (i) bounded for four classes of H-free chordal graphs; (ii) unbounded for three subclasses of split graphs.  ...  graphs of bounded clique-width (recall that perfect graphs form a superclass of chordal graphs).  ... 
doi:10.1007/978-3-662-48054-0_12 fatcat:74newl3elzetxe2kg5rx5bzooe

Clique-Width for Hereditary Graph Classes [article]

Konrad K. Dabrowski, Matthew Johnson, Daniël Paulusma
2019 arXiv   pre-print
Clique-width is a well-studied graph parameter owing to its use in understanding algorithmic tractability: if the clique-width of a graph class G is bounded by a constant, a wide range of problems that  ...  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.  ...  We now present the state-of-the-art summary for well-quasi-orderability for classes on (H 1 , H 2 )-free graphs, which is obtained by combining results from [6, 63, 64, 72, 122, 123] .  ... 
arXiv:1901.00335v2 fatcat:3mb44qloc5cxxddyimwo6horqa
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