Independent arithmetic progressions

15 Jan 2019  ·  Conlon David, Fox Jacob, Sudakov Benny ·

We show that there is a positive constant $c$ such that any graph on vertex set $[n]$ with at most $c n^2/k^2 \log k$ edges contains an independent set of order $k$ whose vertices form an arithmetic progression. We also present applications of this result to several questions in Ramsey theory...

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