The Ramsey number of a long even cycle versus a star

2020/03/06 by Peter Allen, Tomasz Łuczak, Allen, Peter +5 · 3 citations
Mathematics · #05C35 #05C38 (Secondary) #05C55 (Primary) #Advanced Topology and Set Theory #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2003.03310

openalex publication_date 2020/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We find the exact value of the Ramsey number R(C_2ℓ,K_1,n), when ℓ and n=O(ℓ^10/9) are large. Our result is closely related to the behaviour of Turán number ex(N, C_2ℓ) for an even cycle whose length grows quickly with N.

Citations

• Some Theorems on Abstract Graphs

Cited by

• Nikiforov's spectral consecutive cycle problem and the connected-matching method
• An exact Ramsey number of large bipartite graphs versus odd wheel
• Ramsey numbers of long even cycles versus books

Related

• An exact Ramsey number of large bipartite graphs versus odd wheel
• Ramsey numbers of long even cycles versus books
• On Star critical Ramsey numbers related to large cycles versus complete graphs
• An improved upper bound for the multicolour Ramsey number of odd cycles
• Large book--cycle Ramsey numbers