Given a plane graph G (i.e., a planar graph with a fixed planar embedding) and a simple cycle C in G whose vertices are mapped to a convex polygon, we consider the question whether this drawing can be extended to a planar straight-line drawing of G. We characterize when this is possible in terms of simple necessary conditions, which we prove to be sufficient. This also leads to a linear-time testing algorithm. If a drawing extension exists, it can be computed in the same running time. © 2013 Springer International Publishing Switzerland.
CITATION STYLE
Mchedlidze, T., Nöllenburg, M., & Rutter, I. (2013). Drawing planar graphs with a prescribed inner face. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8242 LNCS, pp. 316–327). Springer Verlag. https://doi.org/10.1007/978-3-319-03841-4_28
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