Name
Abstract | ||
|---|---|---|
A geometric simultaneous embedding of two graphs G1 = (V1,E1) and G2 = (V2,E2) with a bijective mapping of their vertex sets γ : V1 → V2 is a pair of planar straight-line drawings Γ1 of G1 and Γ2 of G2, such that each vertex v2 = γ(v1) is mapped in Γ2 to the same point where v1 is mapped in Γ1, where v1 ∈ V1 and v2 ∈ V2. In this paper we examine several constrained versions and a relaxed version of the geometric simultaneous embedding problem. We show that if the input graphs are assumed to share no common edges this does not seem to yield large classes of graphs that can be simultaneously embedded. Further, if a prescribed combinatorial embedding for each input graph must be preserved, then we can answer some of the problems that are still open for geometric simultaneous embedding. Finally, we present some positive and negative results on the near-simultaneous embedding problem, in which vertices are not mapped exactly to the same but to "near" points in the different drawings. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1007/978-3-540-77537-9_27 | Journal of Graph Algorithms and Applications |
Keywords | DocType | Volume |
vertex v2,geometric simultaneous embedding,common edge,near-simultaneous embedding problem,geometric simultaneous embedding problem,bijective mapping,vertex set,near-simultaneous embeddings,graphs g1,different drawing,input graph | Journal | 13 |
Issue | ISSN | ISBN |
3 | 0302-9743 | 3-540-77536-6 |
Citations | PageRank | References |
10 | 0.70 | 14 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Fabrizio Frati | 1 | 462 | 48.60 |
| Michael Kaufmann | 2 | 361 | 25.45 |
| Stephen G. Kobourov | 3 | 1440 | 122.20 |