An efficient algorithm to recognize prime undirected graphs

  • Cournier Alain
  • Habib Michel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 657)


A graph is said to be prime if it has no non-trivial substitution decomposition, or module. This paper introduces a simple but efficient (O(n + m ln n)) algorithm to test the primality of undirected graphs. The fastest previous algorithm is due to Muller and Spinrad [MS89] and requires quadratic time. Our approach can be seen as a common generalization of Spinrad's work on P4-tree structure and substitution decomposition [Spi89] and Ille's one about the structure of prime graphs [Ill90] (see also Schmerl and Trotter [ST91] which contains similar results).


Undirected graphs modules substitution decomposition autonomous subsets prime graphs 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Cournier Alain
    • 1
  • Habib Michel
    • 1
  1. 1.LIRMMMontpellierFrance

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