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- W3190243886 abstract "Abstract We prove Turán-type theorems for two related Ramsey problems raised by Bollobás and by Fox and Sudakov. First, for t ≥ 3, we show that any two-colouring of the complete graph on n vertices that is δ -far from being monochromatic contains an unavoidable t-colouring when δ ≫ n −1/ t , where an unavoidable t -colouring is any two-colouring of a clique of order 2 t in which one colour forms either a clique of order t or two disjoint cliques of order t . Next, for t ≥ 3, we show that any tournament on n vertices that is δ -far from being transitive contains an unavoidable t-tournament when δ ≫ n −1/[ t /2] , where an unavoidable t -tournament is the blow-up of a cyclic triangle obtained by replacing each vertex of the triangle by a transitive tournament of order t . Conditional on a well-known conjecture about bipartite Turán numbers, both our results are sharp up to implied constants and hence determine the order of magnitude of the corresponding off-diagonal Ramsey numbers." @default.
- W3190243886 created "2021-08-16" @default.
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- W3190243886 date "2021-04-26" @default.
- W3190243886 modified "2023-10-18" @default.
- W3190243886 title "Turán theorems for unavoidable patterns" @default.
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- W3190243886 doi "https://doi.org/10.1017/s030500412100027x" @default.
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