Planar and Quasi Planar Simultaneous Geometric Embedding
نویسندگان
چکیده
منابع مشابه
Geometric Simultaneous Embeddings of a Graph and a Matching
The geometric simultaneous embedding problem asks whether two planar graphs on the same set of vertices in the plane can be drawn using straight lines, such that each graph is plane. Geometric simultaneous embedding is a current topic in graph drawing and positive and negative results are known for various classes of graphs. So far only connected graphs have been considered. In this paper we pr...
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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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Let G1 and G2 be a pair of planar graphs such that V (G1) = V (G2) = V . A simultaneous embedding [6] Ψ = (Γ1,Γ2) of G1 and G2 is a pair of crossing-free drawings Γ1 and Γ2 of G1 and G2, respectively, such that for every vertex v ∈ V we have Γ1(v) = Γ2(v). If every edge e ∈ E(G1) ∩ E(G2) is represented with the same simple open Jordan curve both in Γ1 and in Γ2 we say that Ψ is a simultaneous e...
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We consider the following problem known as simultaneous geometric graph embedding (SGE). Given a set of planar graphs on a shared vertex set, decide whether the vertices can be placed in the plane in such a way that for each graph the straight-line drawing is planar. We partially settle an open problem of Erten and Kobourov [5] by showing that even for two graphs the problem is NP-hard. We also...
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عنوان ژورنال:
- Comput. J.
دوره 58 شماره
صفحات -
تاریخ انتشار 2014