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.
Luczak.R(C n, Cn, Cn)≤(4 +o(1))n.Journal of Combinatorial Theory, Series B, 75(2):174–187
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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.