Non-homotopic Loops with a Bounded Number of Pairwise Intersections

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00551784" target="_blank" >RIV/67985807:_____/21:00551784 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-030-92931-2_15" target="_blank" >http://dx.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>

Result language
angličtina
Original language name
Non-homotopic Loops with a Bounded Number of Pairwise Intersections
Original language description
Let V_n be a set of n points in the plane and let x∈V_n . An x-loop is a continuous closed curve not containing any point of V_n . We say that two x-loops are non-homotopic if they cannot be transformed continuously into each other without passing through a point of Vn . For n=2, we give an upper bound e^O(k^(1/2)) 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 O(k^(1/2)) is asymptotically tight. The previous upper bound 2^((2k)^4) was proved by Pach et al. [6]. We prove the above result by proving the asymptotic upper bound e^O(k^(1/2)) for a similar problem when x∈V_n, and by proving a close relation between the two problems.
Czech name
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Czech description
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Project
<a href="/en/project/GJ20-27757Y" target="_blank" >GJ20-27757Y: Random discrete structures</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Graph Drawing and Network Visualization. 29th International Symposium GD 2021, Revised Selected Papers
ISBN
978-3-030-92930-5
ISSN
0302-9743
e-ISSN
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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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