Work

A Polynomial Improvement for the Odd Cycle–Complete Ramsey Numbers

Year: 2026

Type: article

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 .

Source: COMBINATORICA

DOI: 10.1007/s00493-026-00226-x

Authors: Marcelo Campos, Matthew Jenssen, Marcus Michelen, Florian Pfender, Julian Sahasrabudhe

Institutions: Instituto Nacional de Matemática Pura e Aplicada, King's College London, Northwestern University, University of Colorado Denver, University of Cambridge

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: National Science Foundation, HORIZON EUROPE European Research Council