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Clique-width and the speed of hereditary properties

Allen, Peter, Lozin, Vadim and Rao, Michaël (2009) Clique-width and the speed of hereditary properties. The Electronic Journal of Combinatorics, 16 (1). R35. ISSN 1077-8926

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Abstract

In this paper, we study the relationship between the number of n-vertex graphs in a hereditary class X, also known as the speed of the class X, and boundedness of the clique-width in this class. We show that if the speed of X is faster than n!cn for any c, then the clique-width of graphs in X is unbounded, while if the speed does not exceed the Bell number Bn, then the clique-width is bounded by a constant. The situation in the range between these two extremes is more complicated. This area contains both classes of bounded and unbounded clique-width. Moreover, we show that classes of graphs of unbounded clique-width may have slower speed than classes where the clique-width is bounded.

Item Type: Article
Official URL: http://www.combinatorics.org/ojs/index.php/eljc/in...
Additional Information: © 2009 The Author
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 28 May 2012 14:51
URL: http://eprints.lse.ac.uk/44100/

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