---
OA_place: publisher
_id: '8032'
abstract:
- lang: eng
  text: "Algorithms in computational 3-manifold topology typically take a triangulation
    as an input and return topological information about the underlying 3-manifold.
    However, extracting the desired information from a triangulation (e.g., evaluating
    an invariant) is often computationally very expensive. In recent years this complexity
    barrier has been successfully tackled in some cases by importing ideas from the
    theory of parameterized algorithms into the realm of 3-manifolds. Various computationally
    hard problems were shown to be efficiently solvable for input triangulations that
    are sufficiently “tree-like.”\r\nIn this thesis we focus on the key combinatorial
    parameter in the above context: we consider the treewidth of a compact, orientable
    3-manifold, i.e., the smallest treewidth of the dual graph of any triangulation
    thereof. By building on the work of Scharlemann–Thompson and Scharlemann–Schultens–Saito
    on generalized Heegaard splittings, and on the work of Jaco–Rubinstein on layered
    triangulations, we establish quantitative relations between the treewidth and
    classical topological invariants of a 3-manifold. In particular, among other results,
    we show that the treewidth of a closed, orientable, irreducible, non-Haken 3-manifold
    is always within a constant factor of its Heegaard genus."
acknowledged_ssus:
- _id: E-Lib
- _id: CampIT
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Kristóf
  full_name: Huszár, Kristóf
  id: 33C26278-F248-11E8-B48F-1D18A9856A87
  last_name: Huszár
  orcid: 0000-0002-5445-5057
citation:
  ama: Huszár K. Combinatorial width parameters for 3-dimensional manifolds. 2020.
    doi:<a href="https://doi.org/10.15479/AT:ISTA:8032">10.15479/AT:ISTA:8032</a>
  apa: Huszár, K. (2020). <i>Combinatorial width parameters for 3-dimensional manifolds</i>.
    Institute of Science and Technology Austria. <a href="https://doi.org/10.15479/AT:ISTA:8032">https://doi.org/10.15479/AT:ISTA:8032</a>
  chicago: Huszár, Kristóf. “Combinatorial Width Parameters for 3-Dimensional Manifolds.”
    Institute of Science and Technology Austria, 2020. <a href="https://doi.org/10.15479/AT:ISTA:8032">https://doi.org/10.15479/AT:ISTA:8032</a>.
  ieee: K. Huszár, “Combinatorial width parameters for 3-dimensional manifolds,” Institute
    of Science and Technology Austria, 2020.
  ista: Huszár K. 2020. Combinatorial width parameters for 3-dimensional manifolds.
    Institute of Science and Technology Austria.
  mla: Huszár, Kristóf. <i>Combinatorial Width Parameters for 3-Dimensional Manifolds</i>.
    Institute of Science and Technology Austria, 2020, doi:<a href="https://doi.org/10.15479/AT:ISTA:8032">10.15479/AT:ISTA:8032</a>.
  short: K. Huszár, Combinatorial Width Parameters for 3-Dimensional Manifolds, Institute
    of Science and Technology Austria, 2020.
corr_author: '1'
date_created: 2020-06-26T10:00:36Z
date_published: 2020-06-26T00:00:00Z
date_updated: 2026-04-08T07:21:28Z
day: '26'
ddc:
- '514'
degree_awarded: PhD
department:
- _id: UlWa
doi: 10.15479/AT:ISTA:8032
file:
- access_level: open_access
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  creator: khuszar
  date_created: 2020-06-26T10:03:58Z
  date_updated: 2020-07-14T12:48:08Z
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  file_name: Kristof_Huszar-Thesis.pdf
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  date_updated: 2020-07-14T12:48:08Z
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  file_name: Kristof_Huszar-Thesis-source.zip
  file_size: 7163491
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file_date_updated: 2020-07-14T12:48:08Z
has_accepted_license: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '06'
oa: 1
oa_version: Published Version
page: xviii+120
publication_identifier:
  isbn:
  - 978-3-99078-006-0
  issn:
  - 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
  record:
  - id: '6556'
    relation: dissertation_contains
    status: public
  - id: '7093'
    relation: dissertation_contains
    status: public
status: public
supervisor:
- first_name: Uli
  full_name: Wagner, Uli
  id: 36690CA2-F248-11E8-B48F-1D18A9856A87
  last_name: Wagner
  orcid: 0000-0002-1494-0568
- first_name: Jonathan
  full_name: Spreer, Jonathan
  last_name: Spreer
title: Combinatorial width parameters for 3-dimensional manifolds
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2020'
...