On the $(k+2,k)$-problem of Brown, Erdős and Sós

Seminar series

Combinatorial Theory Seminar

Date

Tue, 13 Feb 2024

Time

14:00 - 15:00

Location

Speaker

Oleg Pikhurko

Organisation

University of Warwick

Brown-Erdős-Sós initiated the study of the maximum number of edges in an $n$ -vertex $r$ -graph such that no $k$ edges span at most $s$ vertices. If $s=rk-2k+2$ then this function is quadratic in $n$ and its asymptotic was previously known for $k=2,3,4$ . I will present joint work with Stefan Glock, Jaehoon Kim, Lyuben Lichev and Shumin Sun where we resolve the cases $k=5,6,7$ .