A Ramsey variant of the Brown-Erdős-Sós conjecture
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10438308" target="_blank" >RIV/00216208:11320/21:10438308 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=YUN4DJDPg0" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=YUN4DJDPg0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/blms.12510" target="_blank" >10.1112/blms.12510</a>
Alternative languages
Result language
angličtina
Original language name
A Ramsey variant of the Brown-Erdős-Sós conjecture
Original language description
An (Formula presented.) -uniform hypergraph ((Formula presented.) -graph for short) is called linear if every pair of vertices belongs to at most one edge. A linear (Formula presented.) -graph is complete if every pair of vertices is in exactly one edge. The famous Brown-Erdős-Sós conjecture states that for every fixed (Formula presented.) and (Formula presented.), every linear (Formula presented.) -graph with (Formula presented.) edges contains (Formula presented.) edges spanned by at most (Formula presented.) vertices. As an intermediate step towards this conjecture, Conlon and Nenadov recently suggested to prove its natural Ramsey relaxation. Namely, that for every fixed (Formula presented.), (Formula presented.) and (Formula presented.), in every (Formula presented.) -colouring of a complete linear (Formula presented.) -graph, one can find (Formula presented.) monochromatic edges spanned by at most (Formula presented.) vertices. We prove that this Ramsey version of the conjecture holds under the additional assumption that (Formula presented.), and we show that for (Formula presented.) it holds for all (Formula presented.).
Czech name
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Czech description
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Classification
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)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Bulletin of the London Mathematical Society
ISSN
0024-6093
e-ISSN
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Volume of the periodical
53
Issue of the periodical within the volume
5
Country of publishing house
GB - UNITED KINGDOM
Number of pages
17
Pages from-to
1453-1469
UT code for WoS article
000658418500001
EID of the result in the Scopus database
2-s2.0-85107351287