
Parameterized Algorithms for Book Embedding Problems
A kpage book embedding of a graph G draws the vertices of G on a line a...
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Upward Book Embeddings of stGraphs
We study kpage upward book embeddings (kUBEs) of stgraphs, that is, bo...
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Book Embeddings of kMap Graphs
A map is a partition of the sphere into regions that are labeled as coun...
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Experimental Evaluation of Book Drawing Algorithms
A kpage book drawing of a graph G=(V,E) consists of a linear ordering o...
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Planar Graphs that Need Four Pages
We show that there are planar graphs that require four pages in any book...
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Local and Union Page Numbers
We introduce the novel concepts of local and union book embeddings, and,...
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Book embeddings of Reeb graphs
Let X be a simplicial complex with a piecewise linear function f:X→R. Th...
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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 NPcomplete 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.
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