NP-Completeness Definition

• Definition: A decision problem A is NP-complete if

  • A is in NP
  • A is NP-hard

• Example: Spanning tree of degree 4 is NP-complete.

  • Spanning tree of degree 4 is in NP.
  • Hamiltonian path is a known NP-complete problem.
  • Hamiltonian path is polynomial time reducible to spanning tree of degree 4.

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