Abstract
We show that every n-vertex planar graph admits a simultaneous embedding with no mapping and with fixed edges with any (n/2)-vertex planar graph. In order to achieve this result, we prove that every n-vertex plane graph has an induced outerplane subgraph containing at least n/2 vertices. Also, we show that every n-vertex planar graph and every n-vertex planar partial 3-tree admit a simultaneous embedding with no mapping and with fixed edges.
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Angelini, P., Evans, W., Frati, F., Gudmundsson, J. (2013). SEFE with No Mapping via Large Induced Outerplane Graphs in Plane Graphs. In: Cai, L., Cheng, SW., Lam, TW. (eds) Algorithms and Computation. ISAAC 2013. Lecture Notes in Computer Science, vol 8283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45030-3_18
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DOI: https://doi.org/10.1007/978-3-642-45030-3_18
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