A Simple Linear Time LexBFS Cograph Recognition Algorithm

  • Authors:
  • Anna Bretscher;Derek Corneil;Michel Habib;Christophe Paul

  • Affiliations:
  • bretscher@utsc.utoronto.ca and dgc@cs.toronto.edu;-;michel.habib@liafa.jussieu.fr;paul@lirmm.fr

  • Venue:
  • SIAM Journal on Discrete Mathematics
  • Year:
  • 2008

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Abstract

Recently lexicographic breadth first search (LexBFS) has been shown to be a very powerful tool for the development of linear time, easily implementable recognition algorithms for various families of graphs. In this paper, we add to this work by producing a simple two LexBFS sweep algorithm to recognize the family of cographs. This algorithm extends to other related graph families such as $P_4$-reducible, $P_4$-sparse, and distance hereditary. It is an open question whether our cograph recognition algorithm can be extended to a similarly easy algorithm for modular decomposition.