  Fixed parameter tractable (FPT) algorithms run in time f(p(x)) poly(|x|),
where f is an arbitrary function of some parameter p of the input x and poly is
some polynomial function. Treewidth, branchwidth, cliquewidth, NLC-width,
rankwidth, and booleanwidth are parameters often used in the design and
analysis of such algorithms for problems on graphs.
  We show asymptotically almost surely (aas), there are Omega(n) lower bounds
on the treewidth, branchwidth, cliquewidth, NLC-width, and rankwidth of graphs
drawn from a simple random model. This raises important questions about the
generality of FPT algorithms using the corresponding decompositions.
