S. Bhore, R. Ganian, F. Montecchiani, M. Nöllenburg:

"Parameterized Algorithms for Book Embedding Problems";

Talk: Graph Drawing and Network Visualization, Prag; 2019-09-17 - 2019-09-20; in: "GD 2019: Graph Drawing and Network Visualization", LNCS, 11904 (2019), ISBN: 978-3-030-35801-3; 365 - 378.

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.

http://dx.doi.org/10.1007/978-3-030-35802-0_28

https://publik.tuwien.ac.at/files/publik_284557.pdf

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