The Complexity of Unions of Disjoint Sets

  • Christian Glaßer
  • Alan L. Selman
  • Stephen Travers
  • Klaus W. Wagner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4393)


This paper is motivated by the open question whether the union of two disjoint NP-complete sets always is NP-complete. We discover that such unions retain much of the complexity of their single components. More precisely, they are complete with respect to more general reducibilities.

Moreover, we approach the main question in a more general way: We analyze the scope of the complexity of unions of m-equivalent disjoint sets. Under the hypothesis that NE ≠ coNE, we construct degrees in NP where our main question has a positive answer, i.e., these degrees are closed under unions of disjoint sets.


Chromatic Number SIAM Journal Polynomial Hierarchy Mathematical System Theory Polynomial Time Reducibility 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Christian Glaßer
    • 1
  • Alan L. Selman
    • 2
  • Stephen Travers
    • 1
  • Klaus W. Wagner
    • 1
  1. 1.Universität WürzburgGermany
  2. 2.University at BuffaloUSA

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