Convex Drawings of Plane Graphs of Minimum Outer Apices

  • Kazuyuki Miura
  • Machiko Azuma
  • Takao Nishizeki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3843)


In a convex drawing of a plane graph G, every facial cycle of G is drawn as a convex polygon. A polygon for the outer facial cycle is called an outer convex polygon. A necessary and sufficient condition for a plane graph G to have a convex drawing is known. However, it has not been known how many apices of an outer convex polygon are necessary for G to have a convex drawing. In this paper, we show that the minimum number of apices of an outer convex polygon necessary for G to have a convex drawing is, in effect, equal to the number of leaves in a triconnected component decomposition tree of a new graph constructed from G, and that a convex drawing of G having the minimum number of apices can be found in linear time.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Kazuyuki Miura
    • 1
  • Machiko Azuma
    • 2
  • Takao Nishizeki
    • 2
  1. 1.Faculty of Symbiotic Systems ScienceFukushima UniversityFukushimaJapan
  2. 2.Graduate School of Information SciencesTohoku UniversitySendaiJapan

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