Computing Heegaard genus is NP-hard

David Bachman; Ryan Derby-Talbot; Eric Sedgwick

Computing Heegaard genus is NP-hard

Geometric Topology 2016-11-30 v3

Authors: David Bachman , Ryan Derby-Talbot , Eric Sedgwick

Abstract

We show that {\sc Heegaard Genus $\leq g$ }, 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 {\sc CNF-SAT} to {\sc Heegaard Genus $\leq g$ }.

Keywords

heegaard splittings

Cite

@article{arxiv.1606.01553,
  title  = {Computing Heegaard genus is NP-hard},
  author = {David Bachman and Ryan Derby-Talbot and Eric Sedgwick},
  journal= {arXiv preprint arXiv:1606.01553},
  year   = {2016}
}

Comments

Version for publication. To appear in the collection of papers "A Journey through Discrete Mathematics. A Tribute to Jiri Matousek" edited by Martin Loebl, Jaroslav Nesetril and Robin Thomas, to be published by Springer

Computing Heegaard genus is NP-hard

Abstract

Keywords

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