3 papers
math.CO2026
A polynomial improvement for the odd cycle-complete Ramsey numbers
Marcelo Campos, Matthew Jenssen, Marcus Michelen +2
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 with $k…
math.CO2026
An update on multicolor Ramsey lower bounds
Marcelo Campos, Cosmin Pohoata
Building upon previous works by Conlon-Ferber and Wigderson, Sawin showed a few years ago that upper bounds on the minimum density of independent sets in a -free can be us…
math.CO2025
A new lower bound for the Ramsey numbers
Marcelo Campos, Matthew Jenssen, Marcus Michelen +1
We prove a new lower bound for the off-diagonal Ramsey numbers, \[ R(3,k) \geq \bigg( \frac{1}{3}+ o(1) \bigg) \frac{k^2}{\log k }\, , \] thereby narrowing the gap between the uppe…