# Parameterized Algorithms for Book Embedding Problems

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.

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03/27/2018

### On Dispersable Book Embeddings

In a dispersable book embedding, the vertices of a given graph G must be...
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08/22/2017

### Upward Partitioned Book Embeddings

We analyze a directed variation of the book embedding problem when the p...
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08/30/2017

### Experimental Evaluation of Book Drawing Algorithms

A k-page book drawing of a graph G=(V,E) consists of a linear ordering o...
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04/29/2019

### Graph Planarity Testing with Hierarchical Embedding Constraints

Hierarchical embedding constraints define a set of allowed cyclic orders...
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12/05/2013

### Book embeddings of Reeb graphs

Let X be a simplicial complex with a piecewise linear function f:X→R. Th...
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10/13/2021

### Practice Problems for Hardware Engineers

This book is to help undergraduate and graduate students of electrical a...
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03/15/2018

### Minimizing Crossings in Constrained Two-Sided Circular Graph Layouts

Circular layouts are a popular graph drawing style, where vertices are p...