Triangulating planar graphs while minimizing the maximum degree

  • Goos Kant
  • Hans L. Bodlaender
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 621)


In this paper we study the problem of triangulating a planar graph G while minimizing the maximum degree Δ(G′) of the resulting triangulated planar graph G′. It is shown that this problem is NP-complete. Worst-case lower bounds for Δ(G′) with respect to Δ(G) are given. We describe a linear algorithm to triangulate planar graphs, for which the maximum degree of the triangulated graph is only a constant larger than the lower bounds. Finally we show that triangulating one face while minimizing the maximum degree can be achieved in polynomial time. We use this algorithm to obtain a polynomial exact algorithm to triangulate the interior faces of an outerplanar graph while minimizing the maximum degree.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Goos Kant
    • 1
  • Hans L. Bodlaender
    • 1
  1. 1.Dept. of Computer ScienceUtrecht UniversityTB UtrechtThe Netherlands

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