"Special issue on Selected papers from the Twenty-seventh International Symposium on Graph Drawing and Network Visualization, GD 2019" Parameterized Algorithms for Book Embedding Problems Vol. 24, no. 4, pp. 603-620, 2020. Regular paper. Abstract 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 ${\rm F{\small IXED}-O{\small RDER}~B{\small OOK}~T{\small HICKNESS}}$, or not fixed, called ${\rm B{\small OOK}~T{\small HICKNESS}}$. Both problems are known to be ${\sf NP}$-complete in general. We show that ${\rm F{\small IXED}-O{\small RDER}~B{\small OOK}~T{\small HICKNESS}}$ and ${\rm B{\small OOK}~T{\small HICKNESS}}$ are fixed-parameter tractable parameterized by the vertex cover number of the graph and that ${\rm F{\small IXED}-O{\small RDER}~B{\small OOK}~T{\small HICKNESS}}$ is fixed-parameter tractable parameterized by the pathwidth of the vertex order. Submitted: October 2019. Reviewed: January 2020. Revised: March 2020. Accepted: April 2020. Final: April 2020. Published: December 2020. Communicated by Daniel Archambault and Csaba D. Tóth article (PDF) BibTeX