The Worst-Case Time Complexity for Generating All Maximal Cliques

  • Etsuji Tomita
  • Akira Tanaka
  • Haruhisa Takahashi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3106)


We present a depth-first search algorithm for generating all maximal cliques of an undirected graph, in which pruning methods are employed as in Bron and Kerbosch’s algorithm. All maximal cliques generated are output in a tree-like form. Then we prove that its worst-case time complexity is O(3 n/3) for an n-vertex graph. This is optimal as a function of n, since there exist up to 3 n/3 cliques in an n-vertex graph.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Etsuji Tomita
    • 1
  • Akira Tanaka
    • 1
  • Haruhisa Takahashi
    • 1
  1. 1.Department of Information and Communication EngineeringThe University of Electro-CommunicationsTokyoJapan

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