---
_id: '13165'
abstract:
- lang: eng
text: "A graph G=(V, E) is called fully regular if for every independent set I c
V, the number of vertices in V\\I that are not connected to any element of I
depends only on the size of I. A linear ordering of the vertices of G is called
successive if for every i, the first i vertices induce a connected subgraph of
G. We give an explicit formula for the number of successive vertex orderings of
a fully regular graph.\r\nAs an application of our results, we give alternative
proofs of two theorems of Stanley and Gao & Peng, determining the number of linear
edge orderings of complete graphs and complete bipartite graphs, respectively,
with the property that the first i edges induce a connected subgraph.\r\nAs another
application, we give a simple product formula for the number of linear orderings
of the hyperedges of a complete 3-partite 3-uniform hypergraph such that, for
every i, the first i hyperedges induce a connected subgraph. We found similar
formulas for complete (non-partite) 3-uniform hypergraphs and in another closely
related case, but we managed to verify them only when the number of vertices is
small."
article_number: '105776'
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Lixing
full_name: Fang, Lixing
last_name: Fang
- first_name: Hao
full_name: Huang, Hao
last_name: Huang
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
- first_name: Gábor
full_name: Tardos, Gábor
last_name: Tardos
- first_name: Junchi
full_name: Zuo, Junchi
last_name: Zuo
citation:
ama: Fang L, Huang H, Pach J, Tardos G, Zuo J. Successive vertex orderings of fully
regular graphs. Journal of Combinatorial Theory Series A. 2023;199(10).
doi:10.1016/j.jcta.2023.105776
apa: Fang, L., Huang, H., Pach, J., Tardos, G., & Zuo, J. (2023). Successive
vertex orderings of fully regular graphs. Journal of Combinatorial Theory.
Series A. Elsevier. https://doi.org/10.1016/j.jcta.2023.105776
chicago: Fang, Lixing, Hao Huang, János Pach, Gábor Tardos, and Junchi Zuo. “Successive
Vertex Orderings of Fully Regular Graphs.” Journal of Combinatorial Theory.
Series A. Elsevier, 2023. https://doi.org/10.1016/j.jcta.2023.105776.
ieee: L. Fang, H. Huang, J. Pach, G. Tardos, and J. Zuo, “Successive vertex orderings
of fully regular graphs,” Journal of Combinatorial Theory. Series A, vol.
199, no. 10. Elsevier, 2023.
ista: Fang L, Huang H, Pach J, Tardos G, Zuo J. 2023. Successive vertex orderings
of fully regular graphs. Journal of Combinatorial Theory. Series A. 199(10), 105776.
mla: Fang, Lixing, et al. “Successive Vertex Orderings of Fully Regular Graphs.”
Journal of Combinatorial Theory. Series A, vol. 199, no. 10, 105776, Elsevier,
2023, doi:10.1016/j.jcta.2023.105776.
short: L. Fang, H. Huang, J. Pach, G. Tardos, J. Zuo, Journal of Combinatorial Theory.
Series A 199 (2023).
date_created: 2023-06-25T22:00:45Z
date_published: 2023-10-01T00:00:00Z
date_updated: 2024-01-30T12:03:51Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1016/j.jcta.2023.105776
external_id:
arxiv:
- '2206.13592'
file:
- access_level: open_access
checksum: 9eebc213b4182a66063a99083ff5bd04
content_type: application/pdf
creator: dernst
date_created: 2024-01-30T12:03:10Z
date_updated: 2024-01-30T12:03:10Z
file_id: '14902'
file_name: 2023_JourCombinatiorialTheory_Fang.pdf
file_size: 352555
relation: main_file
success: 1
file_date_updated: 2024-01-30T12:03:10Z
has_accepted_license: '1'
intvolume: ' 199'
issue: '10'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-sa/4.0/
month: '10'
oa: 1
oa_version: Published Version
publication: Journal of Combinatorial Theory. Series A
publication_identifier:
eissn:
- 1096-0899
issn:
- 0097-3165
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Successive vertex orderings of fully regular graphs
tmp:
image: /images/cc_by_nc_sa.png
legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 199
year: '2023'
...
---
_id: '14362'
abstract:
- lang: eng
text: "Motivated by recent applications to entropy theory in dynamical systems,
we generalise notions introduced by Matthews and define weakly weighted and componentwise
weakly weighted (generalised) quasi-metrics. We then systematise and extend to
full generality the correspondences between these objects and other structures
arising in theoretical computer science and dynamics. In particular, we study
the correspondences with weak partial metrics and, if the underlying space is
a semilattice, with invariant (generalised) quasi-metrics satisfying the descending
path condition, and with strictly monotone semi(-co-)valuations.\r\nWe conclude
discussing, for endomorphisms of generalised quasi-metric semilattices, a generalisation
of both the known intrinsic semilattice entropy and the semigroup entropy."
article_number: '114129'
article_processing_charge: No
article_type: original
author:
- first_name: Ilaria
full_name: Castellano, Ilaria
last_name: Castellano
- first_name: Anna
full_name: Giordano Bruno, Anna
last_name: Giordano Bruno
- first_name: Nicolò
full_name: Zava, Nicolò
id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad
last_name: Zava
orcid: 0000-0001-8686-1888
citation:
ama: Castellano I, Giordano Bruno A, Zava N. Weakly weighted generalised quasi-metric
spaces and semilattices. Theoretical Computer Science. 2023;977. doi:10.1016/j.tcs.2023.114129
apa: Castellano, I., Giordano Bruno, A., & Zava, N. (2023). Weakly weighted
generalised quasi-metric spaces and semilattices. Theoretical Computer Science.
Elsevier. https://doi.org/10.1016/j.tcs.2023.114129
chicago: Castellano, Ilaria, Anna Giordano Bruno, and Nicolò Zava. “Weakly Weighted
Generalised Quasi-Metric Spaces and Semilattices.” Theoretical Computer Science.
Elsevier, 2023. https://doi.org/10.1016/j.tcs.2023.114129.
ieee: I. Castellano, A. Giordano Bruno, and N. Zava, “Weakly weighted generalised
quasi-metric spaces and semilattices,” Theoretical Computer Science, vol.
977. Elsevier, 2023.
ista: Castellano I, Giordano Bruno A, Zava N. 2023. Weakly weighted generalised
quasi-metric spaces and semilattices. Theoretical Computer Science. 977, 114129.
mla: Castellano, Ilaria, et al. “Weakly Weighted Generalised Quasi-Metric Spaces
and Semilattices.” Theoretical Computer Science, vol. 977, 114129, Elsevier,
2023, doi:10.1016/j.tcs.2023.114129.
short: I. Castellano, A. Giordano Bruno, N. Zava, Theoretical Computer Science 977
(2023).
date_created: 2023-09-24T22:01:11Z
date_published: 2023-10-25T00:00:00Z
date_updated: 2024-01-30T13:22:04Z
day: '25'
department:
- _id: HeEd
doi: 10.1016/j.tcs.2023.114129
external_id:
arxiv:
- '2212.08424'
isi:
- '001076934000001'
intvolume: ' 977'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: 'https://doi.org/10.48550/arXiv.2212.08424 '
month: '10'
oa: 1
oa_version: Preprint
publication: Theoretical Computer Science
publication_identifier:
issn:
- 0304-3975
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Weakly weighted generalised quasi-metric spaces and semilattices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 977
year: '2023'
...
---
_id: '13182'
abstract:
- lang: eng
text: "We characterize critical points of 1-dimensional maps paired in persistent
homology\r\ngeometrically and this way get elementary proofs of theorems about
the symmetry\r\nof persistence diagrams and the variation of such maps. In particular,
we identify\r\nbranching points and endpoints of networks as the sole source of
asymmetry and\r\nrelate the cycle basis in persistent homology with a version
of the stable marriage\r\nproblem. Our analysis provides the foundations of fast
algorithms for maintaining a\r\ncollection of sorted lists together with its persistence
diagram."
acknowledgement: Open access funding provided by Austrian Science Fund (FWF). This
project has received funding from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme, grant no. 788183,
from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and
from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry
and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35. The authors of
this paper thank anonymous reviewers for their constructive criticism and Monika
Henzinger for detailed comments on an earlier version of this paper.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Sebastiano
full_name: Cultrera Di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera Di Montesano
orcid: 0000-0001-6249-0832
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Geometric characterization
of the persistence of 1D maps. Journal of Applied and Computational Topology.
2023. doi:10.1007/s41468-023-00126-9
apa: Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M.
(2023). Geometric characterization of the persistence of 1D maps. Journal of
Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-023-00126-9
chicago: Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner,
and Morteza Saghafian. “Geometric Characterization of the Persistence of 1D Maps.”
Journal of Applied and Computational Topology. Springer Nature, 2023. https://doi.org/10.1007/s41468-023-00126-9.
ieee: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Geometric
characterization of the persistence of 1D maps,” Journal of Applied and Computational
Topology. Springer Nature, 2023.
ista: Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2023. Geometric
characterization of the persistence of 1D maps. Journal of Applied and Computational
Topology.
mla: Biswas, Ranita, et al. “Geometric Characterization of the Persistence of 1D
Maps.” Journal of Applied and Computational Topology, Springer Nature,
2023, doi:10.1007/s41468-023-00126-9.
short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal
of Applied and Computational Topology (2023).
date_created: 2023-07-02T22:00:44Z
date_published: 2023-06-17T00:00:00Z
date_updated: 2024-03-20T09:36:56Z
day: '17'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/s41468-023-00126-9
ec_funded: 1
file:
- access_level: open_access
checksum: 697249d5d1c61dea4410b9f021b70fce
content_type: application/pdf
creator: alisjak
date_created: 2023-07-03T09:41:05Z
date_updated: 2023-07-03T09:41:05Z
file_id: '13185'
file_name: 2023_Journal of Applied and Computational Topology_Biswas.pdf
file_size: 487355
relation: main_file
success: 1
file_date_updated: 2023-07-03T09:41:05Z
has_accepted_license: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Discretization in Geometry and Dynamics
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
publication: Journal of Applied and Computational Topology
publication_identifier:
eissn:
- 2367-1734
issn:
- 2367-1726
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '15094'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Geometric characterization of the persistence of 1D maps
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: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14226'
abstract:
- lang: eng
text: "We introduce the notion of a Faustian interchange in a 1-parameter family
of smooth\r\nfunctions to generalize the medial axis to critical points of index
larger than 0.\r\nWe construct and implement a general purpose algorithm for approximating
such\r\ngeneralized medial axes."
alternative_title:
- ISTA Master's Thesis
article_processing_charge: No
author:
- first_name: Elizabeth R
full_name: Stephenson, Elizabeth R
id: 2D04F932-F248-11E8-B48F-1D18A9856A87
last_name: Stephenson
orcid: 0000-0002-6862-208X
citation:
ama: Stephenson ER. Generalizing medial axes with homology switches. 2023. doi:10.15479/at:ista:14226
apa: Stephenson, E. R. (2023). Generalizing medial axes with homology switches.
Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14226
chicago: Stephenson, Elizabeth R. “Generalizing Medial Axes with Homology Switches.”
Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14226.
ieee: E. R. Stephenson, “Generalizing medial axes with homology switches,” Institute
of Science and Technology Austria, 2023.
ista: Stephenson ER. 2023. Generalizing medial axes with homology switches. Institute
of Science and Technology Austria.
mla: Stephenson, Elizabeth R. Generalizing Medial Axes with Homology Switches.
Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:14226.
short: E.R. Stephenson, Generalizing Medial Axes with Homology Switches, Institute
of Science and Technology Austria, 2023.
date_created: 2023-08-24T13:01:18Z
date_published: 2023-08-24T00:00:00Z
date_updated: 2024-02-26T23:30:04Z
day: '24'
ddc:
- '500'
degree_awarded: MS
department:
- _id: GradSch
- _id: HeEd
doi: 10.15479/at:ista:14226
file:
- access_level: closed
checksum: 453caf851d75c3478c10ed09bd242a91
content_type: application/x-zip-compressed
creator: cchlebak
date_created: 2023-08-24T13:02:49Z
date_updated: 2024-02-26T23:30:03Z
embargo_to: open_access
file_id: '14227'
file_name: documents-export-2023-08-24.zip
file_size: 15501411
relation: source_file
- access_level: open_access
checksum: 7349d29963d6695e555e171748648d9a
content_type: application/pdf
creator: cchlebak
date_created: 2023-08-24T13:03:42Z
date_updated: 2024-02-26T23:30:03Z
embargo: 2024-02-25
file_id: '14228'
file_name: thesis_pdf_a.pdf
file_size: 6854783
relation: main_file
file_date_updated: 2024-02-26T23:30:03Z
has_accepted_license: '1'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: '43'
publication_identifier:
issn:
- 2791-4585
publication_status: published
publisher: Institute of Science and Technology Austria
status: public
supervisor:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
title: Generalizing medial axes with homology switches
type: dissertation
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2023'
...
---
_id: '11428'
abstract:
- lang: eng
text: The medial axis of a set consists of the points in the ambient space without
a unique closest point on the original set. Since its introduction, the medial
axis has been used extensively in many applications as a method of computing a
topologically equivalent skeleton. Unfortunately, one limiting factor in the use
of the medial axis of a smooth manifold is that it is not necessarily topologically
stable under small perturbations of the manifold. To counter these instabilities
various prunings of the medial axis have been proposed. Here, we examine one type
of pruning, called burning. Because of the good experimental results, it was hoped
that the burning method of simplifying the medial axis would be stable. In this
work we show a simple example that dashes such hopes based on Bing’s house with
two rooms, demonstrating an isotopy of a shape where the medial axis goes from
collapsible to non-collapsible.
acknowledgement: 'Partially supported by the DFG Collaborative Research Center TRR
109, “Discretization in Geometry and Dynamics” and the European Research Council
(ERC), grant no. 788183, “Alpha Shape Theory Extended”. Erin Chambers: Supported
in part by the National Science Foundation through grants DBI-1759807, CCF-1907612,
and CCF-2106672. Mathijs Wintraecken: Supported by the European Union’s Horizon
2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement
No. 754411. The Austrian science fund (FWF) M-3073 Acknowledgements We thank André
Lieutier, David Letscher, Ellen Gasparovic, Kathryn Leonard, and Tao Ju for early
discussions on this work. We also thank Lu Liu, Yajie Yan and Tao Ju for sharing
code to generate the examples.'
article_processing_charge: No
author:
- first_name: Erin
full_name: Chambers, Erin
last_name: Chambers
- first_name: Christopher D
full_name: Fillmore, Christopher D
id: 35638A5C-AAC7-11E9-B0BF-5503E6697425
last_name: Fillmore
- first_name: Elizabeth R
full_name: Stephenson, Elizabeth R
id: 2D04F932-F248-11E8-B48F-1D18A9856A87
last_name: Stephenson
orcid: 0000-0002-6862-208X
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: 'Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. A cautionary tale:
Burning the medial axis is unstable. In: Goaoc X, Kerber M, eds. 38th International
Symposium on Computational Geometry. Vol 224. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik; 2022:66:1-66:9. doi:10.4230/LIPIcs.SoCG.2022.66'
apa: 'Chambers, E., Fillmore, C. D., Stephenson, E. R., & Wintraecken, M. (2022).
A cautionary tale: Burning the medial axis is unstable. In X. Goaoc & M. Kerber
(Eds.), 38th International Symposium on Computational Geometry (Vol. 224,
p. 66:1-66:9). Berlin, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.SoCG.2022.66'
chicago: 'Chambers, Erin, Christopher D Fillmore, Elizabeth R Stephenson, and Mathijs
Wintraecken. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” In 38th
International Symposium on Computational Geometry, edited by Xavier Goaoc
and Michael Kerber, 224:66:1-66:9. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2022. https://doi.org/10.4230/LIPIcs.SoCG.2022.66.'
ieee: 'E. Chambers, C. D. Fillmore, E. R. Stephenson, and M. Wintraecken, “A cautionary
tale: Burning the medial axis is unstable,” in 38th International Symposium
on Computational Geometry, Berlin, Germany, 2022, vol. 224, p. 66:1-66:9.'
ista: 'Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. 2022. A cautionary
tale: Burning the medial axis is unstable. 38th International Symposium on Computational
Geometry. SoCG: Symposium on Computational GeometryLIPIcs vol. 224, 66:1-66:9.'
mla: 'Chambers, Erin, et al. “A Cautionary Tale: Burning the Medial Axis Is Unstable.”
38th International Symposium on Computational Geometry, edited by Xavier
Goaoc and Michael Kerber, vol. 224, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2022, p. 66:1-66:9, doi:10.4230/LIPIcs.SoCG.2022.66.'
short: E. Chambers, C.D. Fillmore, E.R. Stephenson, M. Wintraecken, in:, X. Goaoc,
M. Kerber (Eds.), 38th International Symposium on Computational Geometry, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9.
conference:
end_date: 2022-06-10
location: Berlin, Germany
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2022-06-07
date_created: 2022-06-01T14:18:04Z
date_published: 2022-06-01T00:00:00Z
date_updated: 2023-02-21T09:50:52Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2022.66
ec_funded: 1
editor:
- first_name: Xavier
full_name: Goaoc, Xavier
last_name: Goaoc
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
file:
- access_level: open_access
checksum: b25ce40fade4ebc0bcaae176db4f5f1f
content_type: application/pdf
creator: dernst
date_created: 2022-06-07T07:58:30Z
date_updated: 2022-06-07T07:58:30Z
file_id: '11437'
file_name: 2022_LIPICs_Chambers.pdf
file_size: 17580705
relation: main_file
success: 1
file_date_updated: 2022-06-07T07:58:30Z
has_accepted_license: '1'
intvolume: ' 224'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 66:1-66:9
project:
- _id: fc390959-9c52-11eb-aca3-afa58bd282b2
grant_number: M03073
name: Learning and triangulating manifolds via collapses
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 38th International Symposium on Computational Geometry
publication_identifier:
isbn:
- 978-3-95977-227-3
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
series_title: LIPIcs
status: public
title: 'A cautionary tale: Burning the medial axis is unstable'
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 224
year: '2022'
...