  We investigate crossing minimization for 1-page and 2-page book drawings. We
show that computing the 1-page crossing number is fixed-parameter tractable
with respect to the number of crossings, that testing 2-page planarity is
fixed-parameter tractable with respect to treewidth, and that computing the
2-page crossing number is fixed-parameter tractable with respect to the sum of
the number of crossings and the treewidth of the input graph. We prove these
results via Courcelle's theorem on the fixed-parameter tractability of
properties expressible in monadic second order logic for graphs of bounded
treewidth.
