
Four Pages Are Indeed Necessary for Planar Graphs
An embedding of a graph in a book consists of a linear order of its vert...
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Schematic Representation of Large Biconnected Graphs
Suppose that a biconnected graph is given, consisting of a large compone...
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Upward Partitioned Book Embeddings
We analyze a directed variation of the book embedding problem when the p...
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Distance Measures for Embedded Graphs
We introduce new distance measures for comparing embedded graphs based o...
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Book Embeddings of Nonplanar Graphs with Small Faces in Few Pages
An embedding of a graph in a book, called book embedding, consists of a ...
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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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An Experimental Study of a 1planarity Testing and Embedding Algorithm
The definition of 1planar graphs naturally extends graph planarity, nam...
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Upward Book Embeddings of stGraphs
We study kpage upward book embeddings (kUBEs) of stgraphs, that is, book embeddings of singlesource singlesink directed acyclic graphs on k pages with the additional requirement that the vertices of the graph appear in a topological ordering along the spine of the book. We show that testing whether a graph admits a kUBE is NPcomplete for k≥ 3. A hardness result for this problem was previously known only for k = 6 [Heath and Pemmaraju, 1999]. Motivated by this negative result, we focus our attention on k=2. On the algorithmic side, we present polynomialtime algorithms for testing the existence of 2UBEs of planar stgraphs with branchwidth β and of plane stgraphs whose faces have a special structure. These algorithms run in O(f(β)· n+n^3) time and O(n) time, respectively, where f is a singlyexponential function on β. Moreover, on the combinatorial side, we present two notable families of plane stgraphs that always admit an embeddingpreserving 2UBE.
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