Independent sets in hypergraphs and Ramsey properties of graphs and the integers

0503795 - MÚ 2020 RIV US eng J - Článek v odborném periodiku
Hancock, Robert - Staden, K. - Treglown, A.
Independent sets in hypergraphs and Ramsey properties of graphs and the integers.
SIAM Journal on Discrete Mathematics. Roč. 33, č. 1 (2019), s. 153-188. ISSN 0895-4801. E-ISSN 1095-7146
Institucionální podpora: RVO:67985840
Klíčová slova: Ramsey properties of graphs * hypergraphs
Obor OECD: Pure mathematics
Impakt faktor: 0.750, rok: 2019
Způsob publikování: Omezený přístup
http://dx.doi.org/10.1137/18M119642X

Many important problems in combinatorics and other related areas can be phrased in the language of independent sets in hypergraphs. Recently Balogh, Morris, and Samotij [J. Amer. Math. Soc., 28 (2015), pp. 669-709], and independently Saxton and Thomason [Invent. Math., 201 (2015), pp. 925-992], developed very general container theorems for independent sets in hypergraphs, both of which have seen numerous applications to a wide range of problems. In this paper we use the container method to give relatively short and elementary proofs of a number of results concerning Ramsey (and Turán) properties of (hyper)graphs and the integers.
Trvalý link: http://hdl.handle.net/11104/0295588