Graph Algorithms

Foundations of Software Technology and Theoretical Computer Science

Volume 405 of the series Lecture Notes in Computer Science pp 30-43

Date:

A new class of separators and planarity of chordal graphs

  • P. Sreenivasa KumarAffiliated withDepartment of Computer Science and Automation, Indian Institute of Science
  • , C. E. Veni MadhavanAffiliated withDepartment of Computer Science and Automation, Indian Institute of Science

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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.