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)


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BFMY83]
    Beeri, C., Fagin, R., Maier, D., Yannakakis, M., On the Desirability of Acyclic Database Schemes, JACM 30(3), 479–513,1983.CrossRefGoogle Scholar
  2. [G80]
    Golumbic, M.C., Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980.Google Scholar
  3. [H69]
    Harary, F., Graph Theory, Addison Wesley, Reading, MA, 1969.Google Scholar
  4. [HL89]
    Ho, C., Lee, R.C.T., counting Clique Trees and Computing Perfect Elimination Schemes in Parallel, IPL, 31, 61–68, 1989.Google Scholar
  5. [HT74]
    Hopcroft, J.,Tarjan, R.E., Efficient Planarity Testing, JACM, 21(4), 549–568, 1974.CrossRefGoogle Scholar
  6. [K88]
    Klein, P.N., Efficient Parallel Algorithms for Chordal Graphs, FOCS, 150–161, 1988.Google Scholar
  7. [R72]
    Rose, D., On Simple Characterizations of k-trees, Disc., Math., 7, 317–322, 1972.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

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

Personalised recommendations