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Clique-width for hereditary graph classes

Dabrowski, K.K.; Johnson, M.; Paulusma, D.

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K.K. Dabrowski


Allan Lo

Richard Mycroft

Guillem Perarnau

Andrew Treglown


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 are NP-complete in general can be shown to be polynomial-time solvable on G. For this reason, the boundedness or unboundedness of clique-width has been investigated and determined for many graph classes. We survey these results for hereditary graph classes, which are the graph classes closed under taking induced subgraphs. We then discuss the algorithmic consequences of these results, in particular for the Colouring and Graph Isomorphism problems. 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.


Dabrowski, K., Johnson, M., & Paulusma, D. (2019). Clique-width for hereditary graph classes.

Journal Article Type Article
Acceptance Date Dec 31, 2018
Publication Date Jan 1, 2019
Deposit Date Jan 9, 2019
Publicly Available Date Jan 9, 2019
Journal London Mathematical Society lecture note series
Peer Reviewed Peer Reviewed
Pages 1-56


Accepted Journal Article (621 Kb)

Copyright Statement
This material has been published in revised form in Surveys in Combinatorics 2019 edited by Allan Lo, Richard Mycroft, Guillem Perarnau & Andrew Treglown This version is free to view and download for private research and study only. Not for re-distribution or re-use. © Cambridge University Press

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