منابع مشابه
On Simultaneous Planar Graph Embeddings
We consider the problem of simultaneous embedding of planar graphs. There are two variants of this problem, one in which the mapping between the vertices of the two graphs is given and another in which the mapping is not given. We present positive and negative results for the two versions of the problem. Among the positive results with given mapping, we show that we can embed two paths on an n×...
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We study the problem of optimizing over the set of all combinatorial embeddings of a given planar graph. Our objective function prefers certain cycles of G as face cycles in the embedding. The motivation for studying this problem arises in graph drawing, where the chosen embedding has an important in uence on the aesthetics of the drawing. We characterize the set of all possible embeddings of a...
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A question about 2-complexes, analogous to graph planarity, is whether they can be embedded in 3 dimensions. This is a difficult question. Also, whereas planar graphs always admit straightedge embeddings, it is known that 2-complexes may admit embeddings without admitting flatface embeddings. We consider three methods for straight-edge planar graph layout: barycentric maps (and convex-combinati...
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We revisit the issue of low-distortion embedding of metric spaces into the line, and more generally, into the shortest path metric of trees, from the parameterized complexity perspective. Low-distortion embeddings of a metric space into the line, or into some other “simple” metric space, (that is, a mapping that preserves distances, up to some small multiplicative factor called the distortion) ...
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A graph is of parabolic or hyperbolic type if the simple random walk on the vertices is, respectively, recurrent or transient. A plane triangulation graph is CP-parabolic or CP-hyperbolic if the maximal circle packing determined by the graph packs, respectively, the complex plane C or the Poincar e disk D. We examine the implications that (Gromov) negative curvature carries for determining type...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2007
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-007-1353-4