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International Conference on Foundations of Software Technology and Theoretical Computer Science

FSTTCS 1989: Foundations of Software Technology and Theoretical Computer Science pp 30–43Cite as

A new class of separators and planarity of chordal graphs

  • Graph Algorithms
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 405))

Abstract

We introduce a new class of clique separators, called base sets, for chordal graphs. Base sets of a chordal graph closely reflect its structure. We show that the notion of base sets leads to structural characterizations of planar k-trees and planar chordal graphs. Using these characterizations, we develop linear time algorithms for recognizing planar k-trees and planar chordal graphs. These algorithms are extensions of the Lexicographic_Breadth_First_Search algorithm for recognizing chordal graphs and are much simpler than the general planarity checking algorithm. Further, we use the notion of base sets to prove the equivalence of hamiltonian 2-trees and maximal outerplanar graphs.

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References

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Author information

Authors and Affiliations

  1. Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India

    P. Sreenivasa Kumar & C. E. Veni Madhavan

Authors
  1. P. Sreenivasa Kumar
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  2. C. E. Veni Madhavan
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Editor information

C. E. Veni Madhavan

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© 1989 Springer-Verlag Berlin Heidelberg

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Kumar, P.S., Veni Madhavan, C.E. (1989). A new class of separators and planarity of chordal graphs. In: Veni Madhavan, C.E. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1989. Lecture Notes in Computer Science, vol 405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52048-1_30

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  • DOI: https://doi.org/10.1007/3-540-52048-1_30

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52048-1

  • Online ISBN: 978-3-540-46872-1

  • eBook Packages: Springer Book Archive

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