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Keywords:

  • chordal graph;
  • minimal vertex separator;
  • lexicographic breadth-first search;
  • planar graph

Abstract

The set of minimal vertex separators of chordal graphs is usually obtained by two-phase algorithms. Based on properties of the lexicographic breadth-first search, we propose a new one-phase algorithm. We present also a characterization for planar chordal graphs; using our proposed algorithm as an initial step, the implementation of the recognition algorithm becomes trivial.