Abstract
For graphs G and H, the Ramsey number r(G, H) is the smallest number N, such that any red/blue edge-coloring of \(K_N\) contains either a red copy of G or a blue copy of H. Let \(F_n=K_1+nK_2\) be a fan and \(W_4=K_1+C_4\) be a wheel of order five. In this paper, we show that the Ramsey number \(r(W_4,F_n)=4n+1\) for all sufficiently large n. Moreover, this implies that a large fan \(F_n\) is \(W_4\)-good.
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The authors are indebted with the anonymous referees for their careful reading of the preliminary version of the paper, and for the valuable comments which have led to a significant improvement of the content of this paper.
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Communicated by Ebrahim Ghorbani.
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Hao, Y., You, C. Ramsey Numbers of a Wheel of Order Five Versus Fans. Bull. Iran. Math. Soc. 49, 85 (2023). https://doi.org/10.1007/s41980-023-00833-0
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DOI: https://doi.org/10.1007/s41980-023-00833-0