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Tuesday, August 4, 2020

**Abstract:** Given a positive integer $s$, the $s$-colour size-Ramsey number of a graph $H$ is the smallest integer $m$ such that there exists a graph $G$ with $m$ edges where in any $s$-colouring of $E(G)$ there is a monochromatic copy of $H$. We prove that, for any positive integers $k$ and $s$, the $s$-colour size-Ramsey number of the $k$th power of any $n$-vertex tree is linear on $n$.

This is a joint work with S. Berger, Y. Kohayakawa, G. S. Maesaka, W. Mendonca, G. O. Mota and O. Parczyk.

Please email Sean English at SEnglish (at) illinois (dot) edu for the Zoom ID.