Embedding Graphs Simultaneously with Fixed Edges
نویسنده
چکیده
We show that a planar graph and a tree can always be simultaneously embedded with fixed edges and that two outerplanar graphs generally cannot.
منابع مشابه
Simultaneous Graph Embeddings with Fixed Edges
We study the problem of simultaneously embedding several graphs on the same vertex set in such a way that edges common to two or more graphs are represented by the same curve. This problem is known as simultaneously embedding graphs with fixed edges. We show that this problem is closely related to the weak realizability problem: Can a graph be drawn such that all edge crossings occur in a given...
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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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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...
متن کاملIntersection Graphs in Simultaneous Embedding with Fixed Edges
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...
متن کاملCharacterizations of Restricted Pairs of Planar Graphs Allowing Simultaneous Embedding with Fixed Edges
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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تاریخ انتشار 2006