"Intersection Graphs in Simultaneous Embedding with Fixed Edges"
Technical report by Michael Jünger, Michael Schulz, available as BibTeX Source and in portable document format.
Zentrum für Angewandte Informatik Köln, Lehrstuhl Jünger
Preprint Key:	zaik2009-586
Keywords:	Simultaneous Geometric Graph Embeddings
MSC codes:	05C10
This technical report has 13 pages, was written in March 2009, it has not been published.
Abstract:	We examine the simultaneous embedding with fixed edges problem for two planar graphs G1 and G2 with the focus on their in- tersection 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 pair of pla- nar graphs (G1 , G2 ) with intersection S = G1 ∩ G2 has a simultaneous embedding with fixed edges. We will characterize this set by a detailed study of topological embeddings and finally give a complete list of graphs in this set as our main result of this paper.