@article{f31d67b5a7e549f9a32ab4e4b15fb7a1,

title = "A Ramsey variant of the Brown–Erd{\H o}s–S{\'o}s conjecture",

abstract = "An (Formula presented.) -uniform hypergraph ((Formula presented.) -graph for short) is called linear if every pair of vertices belongs to at most one edge. A linear (Formula presented.) -graph is complete if every pair of vertices is in exactly one edge. The famous Brown–Erd{\H o}s–S{\'o}s conjecture states that for every fixed (Formula presented.) and (Formula presented.), every linear (Formula presented.) -graph with (Formula presented.) edges contains (Formula presented.) edges spanned by at most (Formula presented.) vertices. As an intermediate step towards this conjecture, Conlon and Nenadov recently suggested to prove its natural Ramsey relaxation. Namely, that for every fixed (Formula presented.), (Formula presented.) and (Formula presented.), in every (Formula presented.) -colouring of a complete linear (Formula presented.) -graph, one can find (Formula presented.) monochromatic edges spanned by at most (Formula presented.) vertices. We prove that this Ramsey version of the conjecture holds under the additional assumption that (Formula presented.), and we show that for (Formula presented.) it holds for all (Formula presented.).",

keywords = "05C15, 05C65 (primary)",

author = "Asaf Shapira and Mykhaylo Tyomkyn",

note = "Publisher Copyright: {\textcopyright} 2021 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.",

year = "2021",

month = oct,

doi = "10.1112/blms.12510",

language = "אנגלית",

volume = "53",

pages = "1453--1469",

journal = "Bulletin of the London Mathematical Society",

issn = "0024-6093",

publisher = "John Wiley and Sons Ltd",

number = "5",

}