UNIFORM TURAN DENSITY OF CYCLES

J 2023

UNIFORM TURAN DENSITY OF CYCLES

BUCIC, Matija, Jacob COOPER, Daniel KRÁĽ, Samuel MOHR, David Munha CORREIA et. al.

Základní údaje

Originální název

UNIFORM TURAN DENSITY OF CYCLES

Autoři

BUCIC, Matija (191 Chorvatsko), Jacob COOPER (826 Velká Británie a Severní Irsko, domácí), Daniel KRÁĽ (203 Česká republika, garant, domácí), Samuel MOHR (276 Německo, domácí) a David Munha CORREIA (620 Portugalsko)

Vydání

Transactions of the American Mathematical Society, Providence (USA), American Mathematical Society, 2023, 0002-9947

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.300 v roce 2022

Kód RIV

RIV/00216224:14330/23:00133881

Organizační jednotka

Fakulta informatiky

DOI

http://dx.doi.org/10.1090/tran/8873

UT WoS

000967035900001

Klíčová slova anglicky

EXTREMAL PROBLEMS; TURÁN NUMBER; HYPERGRAPHS; GRAPHS

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 8. 4. 2024 16:25, RNDr. Pavel Šmerk, Ph.D.

Anotace

V originále

In the early 1980s, Erdos and Sos initiated the study of the classical Turan problem with a uniformity condition: the uniform Turan density of a hypergraph H is the infimum over all d for which any sufficiently large hypergraph with the property that all its linear-size subhypergraphs have density at least d contains H. In particular, they raise the questions of determining the uniform Turan densities of K-4((3)-) and K-4((3)). The former question was solved only recently by Glebov, Kral', and Volec [Israel J. Math. 211 (2016), pp. 349-366] and Reiher, Rodl, and Schacht [J. Eur. Math. Soc. 20 (2018), pp. 1139-1159], while the latter still remains open for almost 40 years. In addition to K-4((3)-), the only 3-uniform hypergraphs whose uniform Turan density is known are those with zero uniform Turan density classified by Reiher, Rodl and Schacht [J. London Math. Soc. 97 (2018), pp. 77-97] and a specific family with uniform Turan density equal to 1/27.

Návaznosti

MUNI/A/1081/2022, interní kód MU

Název: Modelování, analýza a verifikace (2023)

Investor: Masarykova univerzita, Modelování, analýza a verifikace (2023)

MUNI/I/1677/2018, interní kód MU

Název: MUNI AWARD in Science and Humanitites 1 (Akronym: MASH 1)

Investor: Masarykova univerzita, MUNI AWARD in Science and Humanitites 1, MASH - MUNI Award in Science and Humanities

Citovat

BUCIC, Matija, Jacob COOPER, Daniel KRÁĽ, Samuel MOHR a David Munha CORREIA. UNIFORM TURAN DENSITY OF CYCLES. Transactions of the American Mathematical Society. Providence (USA): American Mathematical Society, 2023, roč. 376, č. 7, s. 4765-4809. ISSN 0002-9947. Dostupné z: https://dx.doi.org/10.1090/tran/8873.

@article{2386885,
   author = {Bucic, Matija and Cooper, Jacob and Kráľ, Daniel and Mohr, Samuel and Correia, David Munha},
   article_location = {Providence (USA)},
   article_number = {7},
   doi = {http://dx.doi.org/10.1090/tran/8873},
   keywords = {EXTREMAL PROBLEMS; TURÁN NUMBER; HYPERGRAPHS; GRAPHS},
   language = {eng},
   issn = {0002-9947},
   journal = {Transactions of the American Mathematical Society},
   title = {UNIFORM TURAN DENSITY OF CYCLES},
   url = {https://www.ams.org/journals/tran/2023-376-07/S0002-9947-2023-08873-0/},
   volume = {376},
   year = {2023}
}

TY  - JOUR
ID  - 2386885
AU  - Bucic, Matija - Cooper, Jacob - Kráľ, Daniel - Mohr, Samuel - Correia, David Munha
PY  - 2023
TI  - UNIFORM TURAN DENSITY OF CYCLES
JF  - Transactions of the American Mathematical Society
VL  - 376
IS  - 7
SP  - 4765-4809
EP  - 4765-4809
PB  - American Mathematical Society
SN  - 00029947
KW  - EXTREMAL PROBLEMS
KW  - TURÁN NUMBER
KW  - HYPERGRAPHS
KW  - GRAPHS
UR  - https://www.ams.org/journals/tran/2023-376-07/S0002-9947-2023-08873-0/
N2  - In the early 1980s, Erdos and Sos initiated the study of the classical Turan problem with a uniformity condition: the uniform Turan density of a hypergraph H is the infimum over all d for which any sufficiently large hypergraph with the property that all its linear-size subhypergraphs have density at least d contains H. In particular, they raise the questions of determining the uniform Turan densities of K-4((3)-) and K-4((3)). The former question was solved only recently by Glebov, Kral', and Volec [Israel J. Math. 211 (2016), pp. 349-366] and Reiher, Rodl, and Schacht [J. Eur. Math. Soc. 20 (2018), pp. 1139-1159], while the latter still remains open for almost 40 years. In addition to K-4((3)-), the only 3-uniform hypergraphs whose uniform Turan density is known are those with zero uniform Turan density classified by Reiher, Rodl and Schacht [J. London Math. Soc. 97 (2018), pp. 77-97] and a specific family with uniform Turan density equal to 1/27.
ER  -

BUCIC, Matija, Jacob COOPER, Daniel KRÁĽ, Samuel MOHR a David Munha CORREIA. UNIFORM TURAN DENSITY OF CYCLES. \textit{Transactions of the American Mathematical Society}. Providence (USA): American Mathematical Society, 2023, roč.~376, č.~7, s.~4765-4809. ISSN~0002-9947. Dostupné z: https://dx.doi.org/10.1090/tran/8873.

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