A Ramsey variant of the Brown-Erdős-Sós conjecture

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

A Ramsey variant of the Brown-Erdős-Sós conjecture

Popis výsledku v původním jazyce

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.).

Název v anglickém jazyce

A Ramsey variant of the Brown-Erdős-Sós conjecture

Popis výsledku anglicky

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.).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Bulletin of the London Mathematical Society

ISSN

0024-6093

e-ISSN

—

Svazek periodika

53

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

17

Strana od-do

1453-1469

Kód UT WoS článku

000658418500001

EID výsledku v databázi Scopus

2-s2.0-85107351287