UNIFORM TURAN DENSITY OF CYCLES

BUCIC, Matija, Jacob COOPER, Daniel KRÁĽ, Samuel MOHR and David Munha CORREIA. UNIFORM TURAN DENSITY OF CYCLES. Transactions of the American Mathematical Society. Providence (USA): American Mathematical Society, 2023, vol. 376, No 7, p. 4765-4809. ISSN 0002-9947. Available from: https://dx.doi.org/10.1090/tran/8873.

Basic information

• Original name: UNIFORM TURAN DENSITY OF CYCLES
• Authors: BUCIC, Matija (191 Croatia), Jacob COOPER (826 United Kingdom of Great Britain and Northern Ireland, belonging to the institution), Daniel KRÁĽ (203 Czech Republic, guarantor, belonging to the institution), Samuel MOHR (276 Germany, belonging to the institution) and David Munha CORREIA (620 Portugal).
• Edition: Transactions of the American Mathematical Society, Providence (USA), American Mathematical Society, 2023, 0002-9947.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: United States of America
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Impact factor: Impact factor: 1.300 in 2022
• RIV identification code: RIV/00216224:14330/23:00133881
• Organization unit: Faculty of Informatics
• Doi: http://dx.doi.org/10.1090/tran/8873
• UT WoS: 000967035900001
• Keywords in English: EXTREMAL PROBLEMS; TURÁN NUMBER; HYPERGRAPHS; GRAPHS
• Tags: International impact, Reviewed

Abstract

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.

Links

• MUNI/A/1081/2022, interní kód MU: Name: Modelování, analýza a verifikace (2023)

Investor: Masaryk University

• MUNI/I/1677/2018, interní kód MU: Name: MUNI AWARD in Science and Humanitites 1 (Acronym: MASH 1)

Investor: Masaryk University, MASH - MUNI Award in Science and Humanities