Simultaneous Embedding of Planar Graphs
نویسندگان
چکیده
Ignaz Rutter Karlsruhe Institute of Technology 11.
منابع مشابه
Simultaneous Embedding of Embedded Planar Graphs
Given k planar graphs G1,...,Gk, deciding whether they admit a simultaneous embedding with fixed edges (SEFE) and whether they admit a simultaneous geometric embedding (SGE) are NP-hard problems, for k ≥ 3 and for k ≥ 2, respectively. In this talk we consider the complexity of the SEFE problem and of the SGE problem when graphs G1,...,Gk have a fixed planar embedding. In sharp contrast with the...
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Abstract A set of planar graphs share a simultaneous embedding if they can be drawn on the same vertex set V of n vertices in the plane without crossings between edges of the same graph. Fixed edges are common edges between graphs that share the same Jordan curve in the simultaneous drawing. We give a necessary condition for when pairs of graphs can have a simultaneous embedding with fixed edge...
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We examine the simultaneous embedding with fixed edges problem for two planar graphs G1 and G2 with the focus on their intersection S = G1∩G2. In particular, we will present the complete set of intersection graphs S that guarantee a simultaneous embedding with fixed edges for (G1, G2). More formally, we define the subset ISEFE of all planar graphs as follows: A graph S lies in ISEFE if every pa...
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A set of planar graphs share a simultaneous embedding if they can be drawn on the same vertex set V in the Euclidean plane without crossings between edges of the same graph. Fixed edges are common edges between graphs that share the same simple curve in the simultaneous drawing. Determining in polynomial time which pairs of graphs share a simultaneous embedding with fixed edges (SEFE) has been ...
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Simultaneous embedding of planar graphs is related to the problems of graph thickness and geometric thickness. Techniques for simultaneous embedding of cycles have been used to show that the degree-4 graphs have geometric thickness at most two [3]. Simultaneous embedding techniques are also useful in visualization of graphs that evolve through time. The notion of simultaneous embedding is relat...
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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 where the mapping is not given. In particular, we show that without mapping, any number of outerplanar graphs can be embedded simultaneously on an O(n)×O(n) grid, and an outerplanar and general planar gra...
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