, Volume 76, Issue 1, pp 47–67 | Cite as

Extending Convex Partial Drawings of Graphs

  • Tamara MchedlidzeEmail author
  • Martin Nöllenburg
  • Ignaz Rutter


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.


Extension of a partial drawing Fixed cycle Fixed inner face Convex shape Straight-line drawing Linear-time algorithm 



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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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Tamara Mchedlidze
    • 1
    Email author
  • Martin Nöllenburg
    • 1
  • Ignaz Rutter
    • 1
  1. 1.Karlsruhe Institute of Technology (KIT)KarlsruheGermany

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