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Clique-width for hereditary graph classes.

Dabrowski, K.K. and Johnson, M. and Paulusma, D. (2019) 'Clique-width for hereditary graph classes.', in Surveys in Combinatorics 2019. , pp. 1-56.

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.

Item Type:Book chapter
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1017/9781108649094.002
Publisher 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
Date accepted:31 December 2018
Date deposited:09 January 2019
Date of first online publication:June 2019
Date first made open access:29 September 2021

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