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Triangulating planar graphs while minimizing the maximum degree

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Algorithm Theory — SWAT '92 (SWAT 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 621))

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Abstract

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.

This work was supported by the ESPRIT Basic Research Actions of the EC under contract No. 3075 (project ALCOM).

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Authors and Affiliations

  1. Dept. of Computer Science, Utrecht University, P.O. Box 80.089, 3508, TB Utrecht, The Netherlands

    Goos Kant & Hans L. Bodlaender

Authors
  1. Goos Kant
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  2. Hans L. Bodlaender
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Otto Nurmi Esko Ukkonen

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© 1992 Springer-Verlag Berlin Heidelberg

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Kant, G., Bodlaender, H.L. (1992). Triangulating planar graphs while minimizing the maximum degree. In: Nurmi, O., Ukkonen, E. (eds) Algorithm Theory — SWAT '92. SWAT 1992. Lecture Notes in Computer Science, vol 621. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55706-7_22

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  • DOI: https://doi.org/10.1007/3-540-55706-7_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55706-7

  • Online ISBN: 978-3-540-47275-9

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