On the Intersections of Non-homotopic Loops

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00539705" target="_blank" >RIV/67985807:_____/21:00539705 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21240/21:00347406
Result on the web
<a href="https://link.springer.com/chapter/10.1007%2F978-3-030-67899-9_15" target="_blank" >https://link.springer.com/chapter/10.1007%2F978-3-030-67899-9_15</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-67899-9_15" target="_blank" >10.1007/978-3-030-67899-9_15</a>

Result language
angličtina
Original language name
On the Intersections of Non-homotopic Loops
Original language description
Let V={v1,…,vn} be a set of n points in the plane and let x∈V . An x-loop is a continuous closed curve not containing any point of V, except of passing exactly once through the point x. We say that two x-loops are non-homotopic if they cannot be transformed continuously into each other without passing through a point of V. For n=2 , we give an upper bound 2O(k) 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. This result is inspired by a very recent result of Pach, Tardos, and Tóth who proved the upper bounds 216k4 for the slightly different scenario when x∉V .
Czech name
—
Czech description
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
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

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