The Cycle-Complete graph Ramsey numbers

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We find the Ramsey number of a cycle vs. a complete graph when the order of the cycle is at least 4 times as large as the order of the complete graph. This partially confirms a conjecture of Erdős, Faudree, Rousseau, and Schelp made in 1978.
23 pages, accepted in Comb. Prob. and Comp

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