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; Jacob COOPER; Daniel KRÁĽ; Samuel MOHR a David Munha CORREIA

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: 1.200

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14330/23:00133881

Organizační jednotka

Fakulta informatiky

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://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 = {https://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://doi.org/10.1090/tran/8873.

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