  A k-page book embedding of a graph G draws the vertices of G on a line and
the edges on k half-planes (called pages) bounded by this line, such that no
two edges on the same page cross. We study the problem of determining whether G
admits a k-page book embedding both when the linear order of the vertices is
fixed, called Fixed-Order Book Thickness, or not fixed, called Book Thickness.
Both problems are known to be NP-complete in general. We show that Fixed-Order
Book Thickness and Book Thickness are fixed-parameter tractable parameterized
by the vertex cover number of the graph and that Fixed-Order Book Thickness is
fixed-parameter tractable parameterized by the pathwidth of the vertex order.
