---
_id: '185'
abstract:
- lang: eng
text: We resolve in the affirmative conjectures of A. Skopenkov and Repovš (1998),
and M. Skopenkov (2003) generalizing the classical Hanani-Tutte theorem to the
setting of approximating maps of graphs on 2-dimensional surfaces by embeddings.
Our proof of this result is constructive and almost immediately implies an efficient
algorithm for testing whether a given piecewise linear map of a graph in a surface
is approximable by an embedding. More precisely, an instance of this problem consists
of (i) a graph G whose vertices are partitioned into clusters and whose inter-cluster
edges are partitioned into bundles, and (ii) a region R of a 2-dimensional compact
surface M given as the union of a set of pairwise disjoint discs corresponding
to the clusters and a set of pairwise disjoint "pipes" corresponding
to the bundles, connecting certain pairs of these discs. We are to decide whether
G can be embedded inside M so that the vertices in every cluster are drawn in
the corresponding disc, the edges in every bundle pass only through its corresponding
pipe, and every edge crosses the boundary of each disc at most once.
alternative_title:
- Leibniz International Proceedings in Information, LIPIcs
article_number: '39'
author:
- first_name: Radoslav
full_name: Fulek, Radoslav
id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87
last_name: Fulek
orcid: 0000-0001-8485-1774
- first_name: Jan
full_name: Kynčl, Jan
last_name: Kynčl
citation:
ama: 'Fulek R, Kynčl J. Hanani-Tutte for approximating maps of graphs. In: Vol 99.
Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:10.4230/LIPIcs.SoCG.2018.39'
apa: 'Fulek, R., & Kynčl, J. (2018). Hanani-Tutte for approximating maps of
graphs (Vol. 99). Presented at the SoCG: Symposium on Computational Geometry,
Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.39'
chicago: Fulek, Radoslav, and Jan Kynčl. “Hanani-Tutte for Approximating Maps of
Graphs,” Vol. 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.39.
ieee: 'R. Fulek and J. Kynčl, “Hanani-Tutte for approximating maps of graphs,” presented
at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol.
99.'
ista: 'Fulek R, Kynčl J. 2018. Hanani-Tutte for approximating maps of graphs. SoCG:
Symposium on Computational Geometry, Leibniz International Proceedings in Information,
LIPIcs, vol. 99, 39.'
mla: Fulek, Radoslav, and Jan Kynčl. Hanani-Tutte for Approximating Maps of Graphs.
Vol. 99, 39, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, doi:10.4230/LIPIcs.SoCG.2018.39.
short: R. Fulek, J. Kynčl, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2018.
conference:
end_date: 2018-06-14
location: Budapest, Hungary
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2018-06-11
date_created: 2018-12-11T11:45:04Z
date_published: 2018-01-01T00:00:00Z
date_updated: 2021-01-12T06:53:36Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.4230/LIPIcs.SoCG.2018.39
file:
- access_level: open_access
checksum: f1b94f1a75b37c414a1f61d59fb2cd4c
content_type: application/pdf
creator: dernst
date_created: 2018-12-17T12:33:52Z
date_updated: 2020-07-14T12:45:19Z
file_id: '5701'
file_name: 2018_LIPIcs_Fulek.pdf
file_size: 718857
relation: main_file
file_date_updated: 2020-07-14T12:45:19Z
has_accepted_license: '1'
intvolume: ' 99'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 261FA626-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02281
name: Eliminating intersections in drawings of graphs
publication_identifier:
isbn:
- 978-3-95977-066-8
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '7735'
quality_controlled: '1'
scopus_import: 1
status: public
title: Hanani-Tutte for approximating maps of graphs
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: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 99
year: '2018'
...