Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-24T06:42:52.293Z Has data issue: false hasContentIssue false

1 - Clique-width for hereditary graph classes

Published online by Cambridge University Press:  17 June 2019

By
Konrad K. Dabrowski ,
Matthew Johnson  and
Daniël Paulusma
Edited by
Allan Lo ,
Richard Mycroft ,
Guillem Perarnau  and
Andrew Treglown
Allan Lo
Affiliation:
University of Birmingham
Richard Mycroft
Affiliation:
University of Birmingham
Guillem Perarnau
Affiliation:
Universitat Politècnica de Catalunya, Barcelona
Andrew Treglown
Affiliation:
University of Birmingham
HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Summary

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.

Keywords

clique-widthgraph colouringgraph containment relationgraph isomorphismhereditary graph classinduced subgraphwell-quasi-orderabilitywidth parameter
Type
Chapter
Information
Surveys in Combinatorics 2019 , pp. 1 - 56
Publisher: Cambridge University Press
Print publication year: 2019

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×