# Upward Partitioned Book Embeddings

We analyze a directed variation of the book embedding problem when the page partition is prespecified and the nodes on the spine must be in topological order (upward book embedding). Given a directed acyclic graph and a partition of its edges into k pages, can we linearly order the vertices such that the drawing is upward (a topological sort) and each page avoids crossings? We prove that the problem is NP-complete for k> 3, and for k> 4 even in the special case when each page is a matching. By contrast, the problem can be solved in linear time for k=2 pages when pages are restricted to matchings. The problem comes from Jack Edmonds (1997), motivated as a generalization of the map folding problem from computational origami.

## Authors

• 17 publications
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• ### Parameterized Algorithms for Book Embedding Problems

A k-page book embedding of a graph G draws the vertices of G on a line a...
08/23/2019 ∙ by Sujoy Bhore, et al. ∙ 0

• ### Upward Book Embeddings of st-Graphs

We study k-page upward book embeddings (kUBEs) of st-graphs, that is, bo...
03/19/2019 ∙ by Carla Binucci, et al. ∙ 0

• ### Book Embeddings of k-Map Graphs

A map is a partition of the sphere into regions that are labeled as coun...
12/12/2020 ∙ by Franz J. Brandenburg, et al. ∙ 0

• ### Experimental Evaluation of Book Drawing Algorithms

A k-page book drawing of a graph G=(V,E) consists of a linear ordering o...
08/30/2017 ∙ by Jonathan Klawitter, et al. ∙ 0

• ### Planar Graphs that Need Four Pages

We show that there are planar graphs that require four pages in any book...
05/28/2020 ∙ by Mihalis Yannakakis, et al. ∙ 0

• ### Local and Union Page Numbers

We introduce the novel concepts of local and union book embeddings, and,...
07/23/2019 ∙ by Laura Merker, et al. ∙ 0