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.
CITATION STYLE
Bhore, S., Ganian, R., Montecchiani, F., & Nöllenburg, M. (2019). Parameterized Algorithms for Book Embedding Problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11904 LNCS, pp. 365–378). Springer. https://doi.org/10.1007/978-3-030-35802-0_28
Mendeley helps you to discover research relevant for your work.