K.K. Dabrowski
Clique-width for hereditary graph classes
Dabrowski, K.K.; Johnson, M.; Paulusma, D.
Authors
Professor Matthew Johnson matthew.johnson2@durham.ac.uk
Head Of Department
Professor Daniel Paulusma daniel.paulusma@durham.ac.uk
Professor
Contributors
Allan Lo
Editor
Richard Mycroft
Editor
Guillem Perarnau
Editor
Andrew Treglown
Editor
Abstract
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.
Citation
Dabrowski, K., Johnson, M., & Paulusma, D. (2019). Clique-width for hereditary graph classes. https://doi.org/10.1017/9781108649094.002
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 |
DOI | https://doi.org/10.1017/9781108649094.002 |
Files
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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 https://doi.org/10.1017/9781108649094. 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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