Compact Visibility Representation and Straight-Line Grid Embedding of Plane Graphs

  • Huaming Zhang
  • Xin He
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2748)


We study the properties of Schnyder’s realizers and canonical ordering trees of plane graphs. Based on these newly discovered properties, we obtain compact drawings of two styles for any plane graph G with n vertices. First we show that G has a visibility representation with height at most \(\lceil \frac{15n}{16} \rceil\). This improves the previous best bound of n-1. The drawing can be obtained in linear time. Second, we show that every plane graph G has a straight-line grid embedding on an (n − Δ0 − 1) × (n − Δ0 − 1) grid, where Δ0 is the number of cyclic faces of G with respect to its minimum realizer. This improves the previous best bound of (n-1) × (n-1). This embedding can also be found in O(n) time.


Plane Graph Unique Path Interior Vertex Graph Drawing Interior Face 
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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Huaming Zhang
    • 1
  • Xin He
    • 1
  1. 1.Department of Computer Science and EngineeringSUNY at BuffaloBuffaloUSA

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