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Special issue on Selected papers from the Twentyseventh International Symposium on Graph Drawing and Network Visualization, GD 2019
DOI: 10.7155/jgaa.00526
Parameterized Algorithms for Book Embedding Problems
Vol. 24, no. 4, pp. 603620, 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 $k$ halfplanes (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 fixedparameter 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 fixedparameter 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.

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