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{\bf Peter Allen, Vadim Lozin and Micha\"el Rao }
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{\bf Clique-Width and the Speed of Hereditary Properties}
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In this paper, we study the relationship between the number of
$n$-vertex graphs in a hereditary class $\cal X$, also known as the
speed of the class $\cal X$, and boundedness of the clique-width in
this class.  We show that if the speed of $\cal X$ is faster than
$n!c^n$ for any $c$, then the clique-width of graphs in $\cal X$ is
unbounded, while if the speed does not exceed the Bell number $B_n$,
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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