Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, May 05, 2022, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Miloš Trujić

On the size-Ramsey number of grids

For a positive integer s, the s x s grid is a graph with vertex set [s] x [s] and two pairs being adjacent if and only if they differ by one in exactly one coordinate. As grids have certain structural parameters unbounded but are rather simple (bounded degree, bipartite) they serve as an interesting example for developing new techniques in studying size-Ramsey numbers. The size-Ramsey number of a graph H is defined as the smallest integer m for which there exists a graph on m vertices such that every two-colouring of its edges contains a monochromatic copy of H. Together with David Conlon and Rajko Nenadov, we recently showed that the size-Ramsey number of an s x s grid is bounded by O(s^{5/2}), significantly improving the previously best known bound and breaking the 'random graph barrier'.

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