A new class of separators and planarity of chordal graphs
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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
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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