A new approach for the Brown-Erdős-Sós problem

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10512088" target="_blank" >RIV/00216208:11320/25:10512088 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ntLrNu4Q7Q" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ntLrNu4Q7Q</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11856-025-2714-5" target="_blank" >10.1007/s11856-025-2714-5</a>

Result language
angličtina
Original language name
A new approach for the Brown-Erdős-Sós problem
Original language description
The celebrated Brown-Erdős-Sós conjecture states that for every fixed e, every 3-uniform hypergraph with Omega(n^2) edges contains e edges spanned by e + 3 vertices. Up to this date all the approaches towards resolving this problem relied on highly involved applications of the hypergraph regularity method, and yet they supplied only approximate versions of the conjecture, producing e edges spanned by e + O(log e/ log log e) vertices. In this short paper we describe a completely different approach, which reduces the problem to a variant of another well-known conjecture in extremal graph theory. A resolution of the latter would resolve the Brown-Erdős-Sós conjecture up to an absolute additive constant.
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
—
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
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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