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Extending Convex Partial Drawings of Graphs

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Abstract

Given a plane graph G (i.e., a planar graph with a fixed planar embedding and outer face) and a biconnected subgraph \(G^{\prime }\) with a fixed planar straight-line convex drawing, 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, one can be computed in the same running time.

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Acknowledgments

Martin Nöllenburg received financial support by the Concept for the Future of KIT (Grant YIG 10-209). Ignaz Rutter was supported by a fellowship within the Postdoc-Program of the German Academic Exchange Service (DAAD). Part of this work was done within GRADR – EUROGIGA project no. 10-EuroGIGA-OP-003.

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Authors and Affiliations

  1. Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany

    Tamara Mchedlidze, Martin Nöllenburg & Ignaz Rutter

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  1. Tamara Mchedlidze
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  2. Martin Nöllenburg
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  3. Ignaz Rutter
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Correspondence to Tamara Mchedlidze.

Additional information

A preliminary version of this work appeared in the Proceedings of the 21st International Symposium on Graph Drawing (GD 2013) [8].

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Mchedlidze, T., Nöllenburg, M. & Rutter, I. Extending Convex Partial Drawings of Graphs. Algorithmica 76, 47–67 (2016). https://doi.org/10.1007/s00453-015-0018-6

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  • DOI: https://doi.org/10.1007/s00453-015-0018-6

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