Computing Heegaard Genus is NP-Hard

  • David Bachman
  • Ryan Derby-Talbot
  • Eric SedgwickEmail author


We show that Heegaard Genusg, the problem of deciding whether a triangulated 3-manifold admits a Heegaard splitting of genus less than or equal to g, is NP-hard. The result follows from a quadratic time reduction of the NP-complete problem CNF-SAT to Heegaard Genus ≤g.


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Copyright information

© Springer International publishing AG 2017

Authors and Affiliations

  • David Bachman
    • 1
  • Ryan Derby-Talbot
    • 2
  • Eric Sedgwick
    • 3
    Email author
  1. 1.Pitzer CollegeClaremontUSA
  2. 2.Quest UniversitySquamishCanada
  3. 3.School of ComputingDePaul UniversityChicagoUSA

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