Geodesic
Star-Critical Ramsey Numbers for Cycles versus K4
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 2, pp. 381-390

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Given three graphs G, H and K we write K → (G, H), if in any red/blue coloring of the edges of K there exists a red copy of G or a blue copy of H. The Ramsey number r(G, H) is defined as the smallest natural number n such that K_n → (G, H) and the star-critical Ramsey number r_∗(G, H) is defined as the smallest positive integer k such that K_n−1⊔ K_1,k → (G, H), where n is the Ramsey number r(G, H). When n ≥ 3, we show that r_∗(C_n, K_4)=2n except for r_∗(C_3, K_4)=8 and r_∗(C_4, K_4) = 9. We also characterize all Ramsey critical r(C_n, K_4) graphs.
Keywords: Ramsey theory, star-critical Ramsey numbers 
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     title = {Star-Critical {Ramsey} {Numbers} for {Cycles} versus {K\protect\textsubscript{4}}},
     journal = {Discussiones Mathematicae. Graph Theory},
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Jayawardene, Chula J.; Narváez, David; Radziszowski, Stanisław P. Star-Critical Ramsey Numbers for Cycles versus K4. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 2, pp. 381-390. http://geodesic.mathdoc.fr/item/DMGT_2021_41_2_a2/