4-Labelings and Grid Embeddings of Plane Quadrangulations

  • Lali Barrière
  • Clemens Huemer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5849)


Finding aesthetic drawings of planar graphs is a main issue in graph drawing. Of special interest are rectangle of influence drawings.The graphs considered here are quadrangulations, that is, planar graphs all whose faces have degree four.We show that each quadrangulation on n vertices has a closed rectangle of influence drawing on the (n - 2) × (n - 2) grid. Biedl, Bretscher and Meijer [2] proved that every planar graph on n vertices without separating triangle has a closed rectangle of influence drawing on the (n - 1) × (n - 1) grid.Our method, which is completely different from that of [2], is in analogy to Schnyder’s algorithm for embedding triangulations on an integer grid [9] and gives a simple algorithm.


Planar Graph Computational Geometry Interior Vertex Graph Drawing Planar Bipartite Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Lali Barrière
    • 1
  • Clemens Huemer
    • 1
  1. 1.Departament de Matemàtica Aplicada IVUniversitat Politècnica de Catalunya 

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