A polynomial improvement for the odd cycle-complete Ramsey numbers

2025/11/13 by Marcelo Campos, Campos, Marcelo, Matthew Jenssen +7 · 1 citation
Mathematics · Computer Science · #Limits and Structures in Graph Theory #Advanced Topology and Set Theory #Complexity and Algorithms in Graphs

paper · pdf · doi:10.48550/arxiv.2511.10641

Abstract

We give a polynomial improvement to the cycle-complete Ramsey numbers r(C_ℓ,K_k) ≥ k^1+1/(ℓ- 2) + ε_ℓ + o(1), for all fixed odd ℓ > 7 with k → ∞, for some ε_ℓ > 0.

Citations

• Improving R(3,k) in just two bites
• A new lower bound for the Ramsey numbers R(3,k)
• Ramsey numbers and the Zarankiewicz problem
• The asymptotics of r(4,t)
• A note on pseudorandom Ramsey graphs
• Cycle-complete Ramsey numbers
• The early evolution of the H-free process

Cited by

• Disproof of the Odd Hadwiger Conjecture
• Improving R(3,k) in just two bites

Related

• An improved upper bound for the multicolour Ramsey number of odd cycles
• An exponential improvement for Ramsey lower bounds
• Cycle-complete Ramsey numbers
• A note on pseudorandom Ramsey graphs
• The Cycle-Complete graph Ramsey numbers