---
res:
bibo_abstract:
- "In graph theory, as well as in 3-manifold topology, there exist several width-type
parameters to describe how \"simple\" or \"thin\" a given graph or 3-manifold
is. These parameters, such as pathwidth or treewidth for graphs, or the concept
of thin position for 3-manifolds, play an important role when studying algorithmic
problems; in particular, there is a variety of problems in computational 3-manifold
topology - some of them known to be computationally hard in general - that become
solvable in polynomial time as soon as the dual graph of the input triangulation
has bounded treewidth.\r\nIn view of these algorithmic results, it is natural
to ask whether every 3-manifold admits a triangulation of bounded treewidth. We
show that this is not the case, i.e., that there exists an infinite family of
closed 3-manifolds not admitting triangulations of bounded pathwidth or treewidth
(the latter implies the former, but we present two separate proofs).\r\nWe derive
these results from work of Agol, of Scharlemann and Thompson, and of Scharlemann,
Schultens and Saito by exhibiting explicit connections between the topology of
a 3-manifold M on the one hand and width-type parameters of the dual graphs of
triangulations of M on the other hand, answering a question that had been raised
repeatedly by researchers in computational 3-manifold topology. In particular,
we show that if a closed, orientable, irreducible, non-Haken 3-manifold M has
a triangulation of treewidth (resp. pathwidth) k then the Heegaard genus of M
is at most 18(k+1) (resp. 4(3k+1)).@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Kristóf
foaf_name: Huszár, Kristóf
foaf_surname: Huszár
foaf_workInfoHomepage: http://www.librecat.org/personId=33C26278-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-5445-5057
- foaf_Person:
foaf_givenName: Jonathan
foaf_name: Spreer, Jonathan
foaf_surname: Spreer
- foaf_Person:
foaf_givenName: Uli
foaf_name: Wagner, Uli
foaf_surname: Wagner
foaf_workInfoHomepage: http://www.librecat.org/personId=36690CA2-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-1494-0568
bibo_doi: 10.20382/JOGC.V10I2A5
bibo_issue: '2'
bibo_volume: 10
dct_date: 2019^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/1920-180X
dct_language: eng
dct_publisher: Computational Geometry Laborartoy@
dct_title: On the treewidth of triangulated 3-manifolds@
...