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Clique-Width and the Speed of Hereditary Properties

Peter Allen 1 Vadim Lozin 1 Michaël Rao 2
2 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
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!c^n 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.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00808010
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Submitted on : Thursday, April 4, 2013 - 5:02:21 PM
Last modification on : Monday, August 5, 2019 - 3:26:03 PM

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  • HAL Id : lirmm-00808010, version 1

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Peter Allen, Vadim Lozin, Michaël Rao. Clique-Width and the Speed of Hereditary Properties. The Electronic Journal of Combinatorics, Open Journal Systems, 2009, 16 (1), pp.11. ⟨lirmm-00808010⟩

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