A Journey Through Discrete Mathematics pp 59-87 | Cite as

# Computing Heegaard Genus is NP-Hard

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## Abstract

We show that Heegaard Genus ≤ *g*, 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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