UNIFORM TURAN DENSITY OF CYCLES
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | Transactions of the American Mathematical Society |
| MU Faculty or unit | |
| Citation | |
| web | https://www.ams.org/journals/tran/2023-376-07/S0002-9947-2023-08873-0/ |
| Doi | http://dx.doi.org/10.1090/tran/8873 |
| Keywords | EXTREMAL PROBLEMS; TURÁN NUMBER; HYPERGRAPHS; GRAPHS |
| Description | 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. |
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