A Polynomial Improvement for the Odd Cycle–Complete Ramsey Numbers
Abstract
Abstract We give a polynomial improvement to the cycle-complete Ramsey numbers $$\begin{aligned} r(C_{\ell },K_k) \geqslant k^{1+\frac{1}{\ell -2} + \varepsilon _{\ell } + o(1)}, \end{aligned}$$ r ( C ℓ , K k ) ⩾ k 1 + 1 ℓ - 2 + ε ℓ + o ( 1 ) , for all fixed odd $$\ell > 7$$ ℓ > 7 with $$k \rightarrow \infty $$ k → ∞ , for some $$\varepsilon _{\ell } > 0$$ ε ℓ > 0 .
Fields of Study & Subjects
Limits and Structures in Graph Theory
Advanced Topology and Set Theory
Complexity and Algorithms in Graphs
Publication details
- Journal / source
- COMBINATORICA
- Publisher
- Springer Science and Business Media LLC
- Volume
- 46
- Issue
- 5
- Publication date
- 18 September 2026
- Language
- EN