2019/08/23 by Sujoy Bhore, Robert Ganian, Bhore, Sujoy +5 · 1 citation
Computer Science · #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #cs.DS
paper · pdf · doi:10.48550/arxiv.1908.08911
Appears in the Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019)
arxiv created 2019/08/23 · arxiv updated 2019/08/26
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.