Algorithmica

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

Extending Convex Partial Drawings of Graphs

  • Tamara Mchedlidze
  • Martin Nöllenburg
  • Ignaz Rutter
Article
  • 119 Downloads

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.

Keywords

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

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

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

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