Geodesic
The cycle-complete graph Ramsey number r(C₅,K₇)
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 1-2, pp. 129-139

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The cycle-complete graph Ramsey number r(Cₘ,Kₙ) is the smallest integer N such that every graph G of order N contains a cycle Cₘ on m vertices or has independence number α(G) ≥ n. It has been conjectured by Erdős, Faudree, Rousseau and Schelp that r(Cₘ,Kₙ) = (m-1)(n-1)+1 for all m ≥ n ≥ 3 (except r(C₃,K₃) = 6). This conjecture holds for 3 ≤ n ≤ 6. In this paper we will present a proof for r(C₅,K₇) = 25.
Keywords: Ramsey numbers, extremal graphs 
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     title = {The cycle-complete graph {Ramsey} number {r(C₅,K₇)}},
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Schiermeyer, Ingo. The cycle-complete graph Ramsey number r(C₅,K₇). Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 1-2, pp. 129-139. http://geodesic.mathdoc.fr/item/DMGT_2005_25_1-2_a13/