A polynomial improvement for the odd cycle-complete Ramsey numbers
Authors
Marcelo Campos
Matthew Jenssen
Marcus Michelen
Florian Pfender
Julian Sahasrabudhe
Abstract
We give a polynomial improvement to the cycle-complete Ramsey numbers \[ r(C_{\ell},K_k) \geq k^{1+1/(\ell- 2) + \varepsilon_{\ell} + o(1)}, \] for all fixed odd $\ell > 7$ with $k \rightarrow \infty$, for some $\varepsilon_{\ell} > 0$.
