Improved bounds show the Ramsey number for even wheels lies between roughly 5n and 8n plus a constant, while related mixed Ramsey numbers with stars and even cycles are asymptotically determined for large graphs.
New bounds for Ramsey numbers involving graphs with a center
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abstract
Let $F_n$, $W_n$, and $\widehat{K}_n$ be the graphs obtained by joining a vertex to $n$ independent edges, a cycle and a path of order $n-1$, respectively. In this paper, we give new bounds for the Ramsey numbers $R(F_n,F_m)$ and $R(W_n,W_n)$, which improve those due to Chen, Yu, and Zhao [EJC, 2021] and Mao, Wang, Magnant, and Schiermeyer [G&C, 2022], respectively, and establish lower and upper bounds for $R(\widehat{K}_n,\widehat{K}_n)$. Moreover, we present a blow-up technique to establish some new lower bounds for the Ramsey numbers of wheels versus cliques.
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math.CO 1years
2026 1verdicts
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On the Ramsey numbers of wheels, cycles, and stars
Improved bounds show the Ramsey number for even wheels lies between roughly 5n and 8n plus a constant, while related mixed Ramsey numbers with stars and even cycles are asymptotically determined for large graphs.