Claims

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1975_01_01_parsons: Theorems 1 and 2 of Parsons (Trans. Amer. Math. Soc. 1975) give R(C_4,K_{1,q^2+1}) = q^2+q+2 and R(C_4,K_{1,q^2}) = q^2+q+1 for every prime power q, from polarity graphs of projective planes; refereed.

2015_01_24_wu_sun_zhang_radziszowski: Theorem 3 of Wu, Sun, Zhang and Radziszowski (Graphs Combin. 2015) gives R(C_4,K_{1,q^2-2}) = q^2+q-1 for prime powers q >= 3 and, for even q, the values at n = q^2-k-1; refereed.

2017_04_01_zhang_chen_cheng: Theorem 4 of Zhang, Chen and Cheng (Discrete Math. 2017) gives R(C_4,K_{1,q^2-t}) = q^2+q-(t-1) for odd prime powers q and 1 <= t <= 2 ceil(q/4), t not 2 ceil(q/4)-1; refereed.

2017_05_01_zhang_chen_cheng: Theorems 6 and 7 of Zhang, Chen and Cheng (Finite Fields Appl. 2017) give R(C_4,K_{1,n}) at n = (q-1)^2+t for even prime powers q and at n = q(q-1)-t for odd prime powers q; refereed.

2024_09_19_boza: Theorem 10 of Boza's preprint determines R(C_4,K_{1,n}) for n = 27 to 33, 37 and 67, which with the known values gives every n <= 38; a preprint, claimed.

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