Original title: Procesy slabé saturace v multipartitních hypergrafech
Translated title: Weak saturation processes in multipartite hypergraphs
Authors: Rajský, Adam ; Tyomkyn, Mykhaylo (advisor) ; Tancer, Martin (referee)
Document type: Bachelor's theses
Year: 2024
Language: cze
Abstract: [cze] [eng]
Dané hypergrafy H a P, wsat(H, P) označuje najmenší počet hrán v podgrafe H s vlastnosťou, že chýbajúce hrany možno postupne pridať tak, že pridanie každej hrany vytvorí novú kópiu P. V roku 1985 Alon dokázal, že wsat(Kn, P)/n konverguje k vlastnej limite pre akýkoľvek graf P. Tuza sa v roku 1992 domnieval, že platí zobecnenie tejto vety pre r-uniformné hypergrafy a dokázali ho Shapira a Tyomkyn v roku 2021. V tejto práci používame metodológiu, ktorú zaviedli Shapira a Tyomkyn, aby sme dokázali podobnuú vetu, v ktorej H je úplný r-partitný r-uniformný hypergraf. Given hypergraphs H and P, wsat(H, P) denotes the smallest number of edges in a subgraph of H with the property that the missing edges can be sequentially added such that the addition of every edge creates a new copy of P. In 1985 Alon proved that wsat(Kn, P)/n tends to a finite limit for any graph P. A generalisation of this Theorem to r-uniform hypergraphs was conjectured by Tuza in 1992 and proved by Shapira and Tyomkyn in 2021. In this thesis, we use the methodology introduced by Shapira and Tyomkyn to prove a similar theorem when H is a complete r-partite r- uniform hypergraph.
Keywords: wsat|weak saturation|hypergraph|extremal combinatorics; wsat|slabá saturácia|hypergraf|extremálna kombinatorika

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/192078

Permalink: http://www.nusl.cz/ntk/nusl-622779


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Bachelor's theses