We prove that, for every $k\ge2$ and every sufficiently large odd $n$, the induced size--Ramsey number of $C_n$ satisfies \[ \widehat R_{\mathrm{ind}}(C_n;k)=e^{\Theta(k)}n. \] This improves the previous upper bound of $e^{O(k\log k)}n$ and resolves a conjecture of Brada\v{c}, Dragani\'c and Sudakov. We obtain this res...
We determine the $k$-colour size--Ramsey number of even cycles up to absolute constant factors. For every $k\ge2$ and every even $n\ge100\log k$, \[ \widehat R_k(C_n)=\Theta(k^2\log k)n. \] The lower bound follows from the corresponding result of Beke, Li and Sahasrabudhe for paths, while our upper bound improves the p...
Motivated by Erd\H{o}s's conjecture on the Tur\'an number of degenerate bipartite graphs, Brada\v{c}, Janzer, Sudakov and Tomon proved that $ \ex(n,T \Box P)=\Theta_{T,P}(n^{3/2})$ for every nontrivial tree $T$ and every nontrivial path $P$, and conjectured that the same order of magnitude holds for the Cartesian produ...
Lan Wang, Cai-Hong Yang· 0 citations
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