Longest Paths in Random Hypergraphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00554068" target="_blank" >RIV/67985807:_____/21:00554068 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/20M1345712" target="_blank" >http://dx.doi.org/10.1137/20M1345712</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/20M1345712" target="_blank" >10.1137/20M1345712</a>

Result language
angličtina
Original language name
Longest Paths in Random Hypergraphs
Original language description
Given integers k, j with 1 < j < k - 1, we consider the length of the longest j-tight path in the binomial random k-uniform hypergraph Hk(n, p). We show that this length undergoes a phase transition from logarithmic length to linear and determine the critical threshold, as well as proving upper and lower bounds on the length in the subcritical and supercritical ranges. In particular, for the supercritical case we introduce the Pathfinder algorithm, a depth-first search algorithm which discovers j-tight paths in a k-uniform hypergraph. We prove that, in the supercritical case, with high probability this algorithm will find a long j-tight path.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA19-08740S" target="_blank" >GA19-08740S: Embedding, Packing and Limits in Graphs</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

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