WEAKLY SATURATED HYPERGRAPHS AND A CONJECTURE OF TUZA

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10476434" target="_blank" >RIV/00216208:11320/23:10476434 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=eRt.laV4_8" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=eRt.laV4_8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/proc/16197" target="_blank" >10.1090/proc/16197</a>

Result language
angličtina
Original language name
WEAKLY SATURATED HYPERGRAPHS AND A CONJECTURE OF TUZA
Original language description
Given a fixed hypergraph H, let wsat(n, H) denote the smallest number of edges in an n-vertex hypergraph G, with the property that one can sequentially add the edges missing from G, so that whenever an edge is added, a new copy of H is created. The study of wsat(n, H) was introduced by Bollob ' as in 1968, and turned out to be one of the most influential topics in extremal combinatorics. While for most H very little is known regarding wsat(n, H), Alon proved in 1985 that for every graph H there is a limiting constant CH so that wsat(n, H) = (CH + o(1))n. Tuza conjectured in 1992 that Alon's theorem can be (appropriately) extended to arbitrary r-uniform hypergraphs. In this paper we prove this conjecture.
Czech name
—
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
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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)

Project
<a href="/en/project/GA22-19073S" target="_blank" >GA22-19073S: Combinatorial and computational complexity in topology and geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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