Non-homotopic Loops with a Bounded Number of Pairwise Intersections
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F21%3A00355335" target="_blank" >RIV/68407700:21240/21:00355335 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/978-3-030-92931-2_15" target="_blank" >https://doi.org/10.1007/978-3-030-92931-2_15</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-92931-2_15" target="_blank" >10.1007/978-3-030-92931-2_15</a>
Alternative languages
Result language
angličtina
Original language name
Non-homotopic Loops with a Bounded Number of Pairwise Intersections
Original language description
Let ???????? be a set of n points in the plane and let ????∉????????. An x-loop is a continuous closed curve not containing any point of ????????. We say that two x-loops are non-homotopic if they cannot be transformed continuously into each other without passing through a point of ????????. For ????=2, we give an upper bound ????????(????root ) on the maximum size of a family of pairwise non-homotopic x-loops such that every loop has fewer than k self-intersections and any two loops have fewer than k intersections. The exponent ????(????root ) is asymptotically tight. The previous upper bound 2(2????)4 was proved by Pach et al. [6]. We prove the above result by proving the asymptotic upper bound ????????(????root ) for a similar problem when ????element????????, and by proving a close relation between the two problems .
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/EF16_019%2F0000765" target="_blank" >EF16_019/0000765: Research Center for Informatics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Graph Drawing and Network Visualization
ISBN
978-3-030-92931-2
ISSN
0302-9743
e-ISSN
1611-3349
Number of pages
13
Pages from-to
210-222
Publisher name
Springer
Place of publication
Cham
Event location
Tübingen
Event date
Sep 14, 2021
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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