A new class of separators and planarity of chordal graphs

  • P. Sreenivasa Kumar
  • C. E. Veni Madhavan
Graph Algorithms
Part of the Lecture Notes in Computer Science book series (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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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • P. Sreenivasa Kumar
    • 1
  • C. E. Veni Madhavan
    • 1
  1. 1.Department of Computer Science and AutomationIndian Institute of ScienceBangaloreIndia

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