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arXiv · 1308.3370

Drawing Planar Graphs with a Prescribed Inner Face

Tamara Mchedlidze·Martin Nöllenburg·Ignaz Rutter
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Abstract

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.

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Tamara Mchedlidze, Martin Nöllenburg, Ignaz Rutter. 2013-08-15. Drawing Planar Graphs with a Prescribed Inner Face. https://arxiv.org/abs/1308.3370

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